I can vouch for David here. I have been in close contact with Ralph Baer for the last two years, and even in this short time, he's begun to mix up his numbers and dates more and more. Considering his age, that's perfectly excusable. Otherwise, he's still sharp as a tack.
Ultimately, the answer to "who was first with what" is always difficult, and in this case, it always comes down to how you define "video game" or "computer game." So if you want to, you can manipulate the definition however you like to make almost any game fit the bill.
You can get more factual about true firsts by using more precise definitions, though. For example, Ralph Baer created the first electronic game to use a standard consumer TV set as a display in 1967 -- and that's a documented fact. But once you go beyond the precise facts into imprecise terminology, things start to get fuzzy: for example, in doing what I stated above, it is almost certain that Baer also created the first electronic game to use a video display. But here, you've already got problems. Some people can probably finagle a weird definition of "video," which was never completely set in stone, but was almost always used -- prior to the 1980s -- to describe electronic signals on a raster-scan CRT display designed to show moving images (ala "television"). So Baer's games were the first to use video displays as they understood them at the time, but even now, it's still not case closed -- as display technology has changed, the conventional use of the term "video" has changed as well. This, in turn, has retroactively broadened the reach of the term "video game" along with it. And so on, and so on. It never really ends.
I expressed my thoughts on this topic with more depth in "Video Games Turn Forty" at 1UP.com (published in 2007). You guys might find it interesting (see pages 4 and 5):
http://www.1up.com/do/feature?pager.offset=0&cId=3159462
Also, regarding the origin of the term "video game," I asked Nolan Bushnell this in an interview a few years ago. You can read his answer here:
http://www.vintagecomputing.com/index.php/archives/404
Of course, his memory could be completely wrong. Interestingly enough, we also discussed Ralph Baer in that interview.
-- Benj