That's a macho line of popular bullshit that sounds super-hardcore but doesn't really address anything useful. Overtraining could be under-recovery. It could also be inefficient program design and/or terrible nutrition and/or other outside factors (even simple mental stress). "Under-recovery" is a vague term that's just a side effect of a more direct cause.
If it's the Men's Health article from last week, it was 1x50 per side (for 100 total reps) with 15-25 pounds, alternating arms each rep. That's still a major workout for the core, hips, and shoulder stabilizers. If you didn't work up to it and just jumped into 1x50 on day one, you'd absolutely be wrecked from it and future training that week would be impaired.
If you did build up to it by starting with, say, 1x5-10 per side, then we're talking about something more reasonable. Though that brings up the question of why we'd want to add volume simply for the sake of added volume.
I've often said that TGUs remind me of a kind of weighted yoga. So in that sense, I can understand what the coach was trying to get at. But if that was the goal, I'd still rather implement them as lighter low-rep work at the start of a session instead of a high-rep kinda-sorta cardio/kinda-sorta yoga hybrid.
With all due respect, you need to get a life. If your existence outside the gym is "boring" simply because you're not working out, you're literally missing the point of being alive.
Then have the self-discipline to do full-fledged mobility work, not mobility work disguised as a dumbbell exercise. A basic full-body mobility routine that gives a little extra attention to whatever your individual problem areas are shouldn't take much longer than the TGUs would have. You could even pare it down to only address your problem areas and get it done faster.