Taking classes may or may not be convincing, but teaching duties should be proof enough that you are present at the university. While you can always find replacements for two or even three lectures (usually if you have to go to conferences), it would be hard to do so for the whole academic term.
I wonder now, since CBSA pretty much records every entry, with or without passport stamp, pretty much any trace of activities that requires you to be present at one particular time (teaching, dentist appointment, thesis defence, swiping health card, etc), should be a definite proof that you are continuously present in the country between the date of last entry and the date of the said activity. What's the point then, in providing more proof of my residence for any period in between these two dates (unless specifically requested as per the checklist)?
Unless you somehow acquire the ability to teleport to bypass entry check, or someone else has a shapeshifting power, let's say, if you defended your thesis on July 9 2013, and your last entry to Canada was back on July 1 2010, wouldn't that be enough to prove that you have been continuously present in Canada from July 1 2010 to July 9 2013, even if you had not provided any trace of existence or activities in between (of course, you should still prove that you are enrolled in the study program to begin with)?
Can anybody find a hole in this argument? Of course, one can always argue that I can just bribe the whole department to collude, and buy my degree, but I think it would be way too far-fetched.