In addition to the answers provided by Ross Millikan and timtfj, both of which point out that the odds of a match are in fact far greater than you think, I would like to point out that I think there is also a good bit of psychology at work here.
For example, you noted that the last two digits were $99$. Well, that's a pretty striking combination of digits; more striking than something like $36$. So, in a way, your brain went like
"Hey, interesting, $99$ ... and wow, there is $99$ again! My God!"
But would your brain have lit up that same way had both accounts ended with $36$? Probably not, or at least less so. In other words, your perception on the 'unlikeliness' of this event was partially driven by the nature of these very numbers; you probably would not have perceived both accounts to both end with $36$ to be as equally unlikely ... even though mathematically it is.
Although, maybe I should take that latter part back: I don't know how those passwords are generated, but if that was something chosen by the users themselves, then maybe both accounts ending in $99$ was in fact more likely to happen than both accounts ending in $36$, since people are more likely to choose passwords that have some kind of pattern to it they can remember. Indeed, if this is the case, then the probability of no one else matching $99$ at the end is even smaller than the calculations by timtjf actually show!
Finally, how long were these passwords? If there were lots of digits (or other characters) there, note that there would have been even more possible matches with digits of other characters. So the fact that it was the last two digits, rather than any pair of digits, probably did a good bit of psychological work as well: had the second and third digit of each password have been $99$, you probably would not have been that surprised, and you might in fact not even noticed it.
In the end, then, I am saying that something psychologically jumped out at you, but we tend to give that far more importance than it should. Millions of events happen every day ... and most of them don't jump out at us. But out of those millions, some of them are bound to be a little 'weird', 'unusual', and do jump out at us. Does that mean anything? Probably not.