But why didn't they ask some snipers to resign from the armed forces and then hire them in the police force and deploy them?
In a Hollywood movie the police would call up the local army base who would have a crack team of snipers just sitting around. Some weaselly lawyer would point out it's illegal until some clever grunt suggests "why don't we just resign?" which they would at the drop of a hat. The snipers would race over with their sniper rifles, salute a few times, and take up positions. The kidnappers would all be killed. Heroic music plays. Roll credits.
Reality doesn't work like that. It moves a lot slower and clever legal tricks don't work.
Legality
The plan would likely be highly illegal.
Intent is very important in law. Technicalities don't save you if it can be shown you intended to violate the law. A court would easily show the Munich Police's intent to use the military on domestic soil both through official communications and timing of their resignations.
A law is not just its text, it is also its intent and case law. A judge looking at the ban on using the military domestically would likely object to the technicality of having them resign first violates the intent of the law.
Finally, there would also be the issue of the precedent they're setting. Laws, let alone Constitutional Laws, are not something you simply set aside in a crisis. If the police can ignore the Basic Law because there's a bad situation they weren't prepared for, this would set a very bad precedent for future police violations of Basic Law. Perhaps they could get special dispensation just this one time, but as we'll see below, they didn't have the time.
Morality
Western democracies are built on separation of powers, and they have very, very good reasons to keep the military separate from domestic affairs lest they take over. Particularly Germany who lived through the militarization of their Republic just 30 years prior. It's highly unlikely the Munich Police would have considered it morally acceptable to bring in the military on a technicality.
Just Six Hours
The speed at which this developed, the chaos and changing plans, and the breakdown of communications. Between 4:30am when the hostages were taken and 10:30pm when they were being moved to their helicopters is just 18 hours. This is not a lot of time in 1972.
But really they had less than 6 hours to arrange the airport ambush.
The original plan was to have a squad of police storm the compound by crawling through roof vents. At 4:30pm they entered the compound. The operation was blown when news crews broadcast them on live TV.
After this, plus getting frustrated by the negotiations, the kidnappers now demand to be flown to Cairo. The police saw this as an opportunity to ambush the kidnappers while they're transferring to the plane in the open spaces of an airport. They had to put this all together in less than six hours.
The New Plan Goes South
The new plan was to have the kidnappers and hostages fly in helicopters to the airport and board a waiting 727. It was expected that two kidnappers would inspect the plane where they'd be overpowered by German police waiting inside. Snipers would then take out the remaining kidnappers in the helicopters, expected to be just two or three.
It turns out there were eight kidnappers.
To make matters worse, at the last minute the police aboard the plane voted to abandon their mission, but didn't inform central command. The kidnappers find the aircraft empty and realized it's a trap!
Only now did it all fall on five untrained snipers to take out eight kidnappers.
No Cell Phones, No Internet, No Liaison
But let's say they did decide to use military snipers. What would they have had to do in the six hours between Operation Sunshine failing and cooking up the new airport ambush?
Something easily forgotten is how hard it was in 1972 to not only get in touch with somebody, but to find out how to get in touch with them, or who you're supposed to get in touch with. They'd be using personal contacts, phone books, and land lines.
The Munich Police had no reason to have an army liaison, they'd have to start cold. Who do they call? Once they figure that out, how do they get in touch with them? Whomever they contact would likely need to get authorization for such an unusual request; who do they call? Those officers would have to deliberate about such an unusual request, legally and morally. And so on.
Assuming they get the legal authorization for this plan, now the military has to not only find a team of readily available snipers. Snipers were not nearly as common in 1972 as they are now.
Not just any snipers. They'd have to find ones who are willing to resign from their career in the military on a moment's notice. Probably resign permanently because it would really play havoc with the law if they could just reenlist. If not already on base, they'd have to be found and recalled. Then do all the paper work to make the resignation official.
Then get them from wherever they are to Munich. If they're in, say, Frankfurt that's 4 hours by car.
Snipers vs Designated Marksmen
As a brief aside, most folks mix up Designated Marksmen and Snipers.
Snipers are highly specialized strategic assets. They're trained to operate alone (with a spotter) using camouflage, concealment, and fieldcraft to stay hidden. They provide intelligence and, if necessary, kill high-value targets. They often use specialized rifles, ammunition, and equipment. They operate independently and answer to higher levels of command, such as a battalion.
Designated Marksman are a normal member of an infantry squad who has received additional marksman training. They operate with the squad as a flexible asset for the squad commander, but can still fill all the normal infantry roles. A designated marksman's weapon will be optimized for longer range than normal (300 to 800 meters), but still use the same ammunition as everyone else.
Munich required people trained to operate within a larger group under strict command and control. Once the firing started things would rapidly get chaotic, so they'd also need to operate as infantry. As such, a designated marksman would be more appropriate than a sniper.
Integrating Outsiders
Ok, we have our snipers marksmen.
Now these two groups who have never worked nor trained together have to pull off a tense rescue operation on an extremely tight time scale.
Because they're no longer military they probably couldn't have brought their military equipment, so they need to be equipped. They'll have to familiarize themselves with Munich Police radios. The Munich Police have no special marksmen equipment, so they'll have to use the normal G3 battle rifle with no scopes hampering their ability as a marksmen. But at least it's the rifle they're familiar with.
Once that's done they'll have to be familiarized with the Munich Police's procedures, people, communications, and command. And the Munich Police command would have to be briefed on the capabilities and limitations of these army snipers in order to incorporate them into their plan. And they'd need to be in position and out of sight well before the kidnappers arrived at the airport.
GSG 9
This is all why Germany formed GSG 9. They couldn't use the army. Even if they could, they couldn't slap military and police units with different equipment and procedures who have never trained together in a few hours and expect them to succeed in tense, precision operations.