There are two ways to approach your question: with or without dualism. I will highlight the dualist approach since it is more salient. Keep in mind that I do not find this approach reasonable, and doubt my summary will do it justice.
You might be interested in the concept of philosophical zombie, it is a modal argument against physicalism in the spirit of Saul Kripke that was polished by David Chalmers in The Conscious Mind. The basic idea is that you can have a zombie which is behaviorally equivalent to a human (including making utterances like "Ouch, I feel pain") yet it does not actually experience those emotions. There is nothing that if "feels like" to be a zombie. A zombie can say "I feel sad" and act like it is sad, but it doesn't feel anything.
If you adopt this stance it often becomes impossible to make a good theory-of-mind since everyone except yourself could actually be a zombie. In fact, Chalmers takes this further by talking about a whole parallel Z-universe where all creatures are zombies (including a copy Chalmers that goes around talking about a parallel universe). From this perspective, David's statement can be perfectly valid.
A second approach is looking at this point from the polar opposite perspective: behaviorism. Here, "to understand human emotion" would mean to be able to make predictions of human behavior based on knowledge that the human asserts to be in a certain emotional state. To "feel human emotion" would not be as well defined, but would be roughly equivalent to make the same patterns of behavior as a human that asserts to feel a certain emotion would usually make.
It is easy to see how David's statement can be perfectly valid from this perspective: if David simple stood in the corner and wrote down predictions of what the humans around him would do, then a behaviorist would say that David "understands human emotion". However, since standing in a corner and making predictions while your crew is eaten by aliens is not a typical human response, the behaviorist could conclude that David does not "feel human emotion" (if the behaviorist was tricked into using the word 'feel').
What I provided are two extreme philosophical stances, and each individual lays somewhere in between the two in terms of their personal philosophy on this issue (and maybe some lay on other extremes I did not imagine). Unfortunately, a scientific answer will come down to definitions and semantics. It will depend on what definition of 'feeling' the scientists in question find more reasonable.
