are half of "H2SO4 pH sample problem" webpages just wrong, or am I wrong?
...and you didn't even get into the fact that almost all explanations will ignore the autodissociation of water!

In some cases your online resources will be wrong, of course, and it would be odd to expect uniform correctness in something people donate for free on the Internet (including here BTW).  So that's worth keeping in mind.

However, it's also the case that it is not always important to treat a problem in all its subtlety.  For example, the difference you get in the calculated pH of 1M H2SO4 by treating or ignoring the second dissociation equilibrium is likely to be smaller than your measurement error in a typical undergraduate lab.  So why bother?  On the other hand, if you were running a very careful experiment with 0.01 M H2SO4 you might well want to take those other equilibria into account, and if you were doing something super sensitive with 10^-7 M H2SO4 then you'll need to worry about the autoionization of water, too.

Generally we use the least complex model that gets us the answer consistent with our measurement limitations.  That maximizes insight and reduces the obfuscation of complex calculation, which can easily make it so we fail to recognize an erroneous answer.   This runs all through science and engineering, and it's why simple models have such great staying power even when they are superseded by more sophisticated understanding.  Naturally a concomitant is that the good scientist must become very adept at identifying the least complex model he can use.  That takes deep insight into the limitations of each model, the probable sources of error, the limits of measurement, and the quality of data on hand.  Being good at this is a much more important skill in the senior scientist than mastering the details of the most complex and realistic model there is.