I've heard a lot of stories of ridiculous rule-by-HR culture, but that's so extreme it sounds made up.
Of course, had I known about these practices in advance, I would have declined the job offer. But I didn't. I ended up quitting a few weeks later anyway.
IT would monitor all connections from all employees and send a report to upper management with summary statistics, on a monthly basis.
I was told this was the case by a fellow worker during my second day there, so I tunneled my traffic through my home server via SSH. When IT asked me why I had zero HTTP requests, I reminded them that monitoring employees traffic was illegal under our current legislation. Doing this in a university-like non-profit research center is hard to justify.
Couldn't you just say "I just dont use http anymore because this X company data is very valuable to me" ?
Invert the scenario: if they told you that you had to do work-based research on your own personal Internet connection, would that be OK? Any overage charges are yours to pay, no compensation.
The other part about log analysis seems crazy, though, I agree with you on that.
That sounds batshit insane.