I've heard the story on the news, but just to make sure I wasn't missing something I just went and read it (and a related one). It looks to me as if he overestimated the ability of most people hearing the remark to sort out what, exactly, he was comparing to what. I could be wrong. I'm not a mind-reader any more than anyone else.
It struck me that he may have used Disney because it's a well known, well respected, "outfit" when it comes to processing huge numbers and aiming for "customer" satisfaction, etc. etc. To me, this guy was clearly making the point about what's important to factor in when measuring something like efficiency, process, etc. It was probably careless of him to assume that everyone would "get" exactly what he was comparing to what (and maybe why he chose Disney as his version of, maybe, efficiency, numbers with other important factors to be considered as well).
If I'm right with my own take on why he'd choose to refer to Disney I think the only thing he's really "guilty" of is over-estimating the ability of many people to sort out that (maybe) he wasn't comparing the Veterans' thing to Disneyland; but referring to it (again, maybe) as an easy and well known example of what skilled and experienced people (yes, in this case, at Disney) factor in when THEY'RE aiming for the most effective/efficient/skilled factors that must be considered as part of measuring how good or poor a process is/isn't.
There is a thing in human nature that tends to make many people jump to the conclusion that someone who says or does something they don't understand and may misinterpret (but even if they just take it at face value and don't even consider the possibility of misinterpreting it) is "stupid".
I give people benefit of doubt before automatically just thinking they're stupid; because most people are not stupid (then again, it's very easy for someone who doesn't automatically assume everyone is stupid to, in fact, overestimate many people.
Now he probably can't come out and say, "Sorry, I thought more of you would understand exactly what I was comparing and why I thought it made a good example." Maybe, however, he should have anticipated that everyone wouldn't understand such a "happy" reference. So to me, an apology for the remark ought to do it.
No, he shouldn't resign.