Not to throw any fuel on this fire, but I thought this was worth a quick look. The assertion is pretty straightforward - that high assist totals will be independent of high rebound totals will be independent of high scoring totals, and thus one can calculate the probability with a simple multiplication:
P(triple-double) = P(10+ pts) * P(10+ rebs) * P(10+ asts)
Now, I doubt anybody would say these stats should be 100% independent. For instance, there will obviously be a factor of minutes per game - the more minutes you play the more likely you are to notch high totals (last night was an example, as IT didn't complete the triple-double until overtime). But they should be relatively independent, right?
Well, it seemed to me that the obvious thing to do is to look at a lot of data, and the obvious way to look at a lot of data is to look at Jason Kidd. Kidd notched 107 triple-doubles in his career over 1391 games. That's definitely a big enough sample size that we can make some conclusions. Kidd ended up having 887 games of 10+ points, 569 games of 10+ assists, and 216 games of 10+ rebounds. I'll spare the math, but the result is that if an independent calculation sufficed, Kidd would have been expected to record only 56 triple-doubles - he got almost twice as many.
Clearly independent multiplication does not suffice. Lots of factors could play a role - in addition to playing time, there's quality of opponent, there's the artificial benchmark effect (Kidd's coaches are more likely to leave him in if he's close to a triple-double; Kidd's teammates are more likely to consciously concede a rebound to him if he's close, etc.), and there are probably other things I haven't thought of.
Determining how all of those factors play together to determine a player's "true probability" of getting a triple-double would take massive amounts of time that I'm not willing to put in, but it's probably not as simple as just saying, "Oh, multiply by 2". For his own part, IT would be expected to have 0.04 triple-doubles at this point, which would suggest (but is way too small of a sample size to make a solid conclusion) that players who do not approach triple-double stats often are much more than twice as likely to get a triple-double than the independence assumption would suggest.