Coupl'a points on the ravings of others
1) The Kursk: This incident has no bearing on the Kursk tragedy. Even at the time, everyone already knew that there was an American sub in the area, spying on the Russian fleet operations. Which means it had to get damn close, leading everyone to suspect that a collision was the cause of the disaster.
Due to the partial failure of the salvaging operation, there will probably never be a definitive answer: The USA insists that it was a dud torp (and poor sub design) and the Russians will insist that it was a collision with a nosey and irresponsible Yank sub.
2) The subs deliberately shadowing each other: If this really was the case, one or both captains would deserve to be shot! Hunting boomers is a job for dedicated attack subs, not for other boomers.
A boomer's job is to be always ready to destroy a small country at a moment's notice*. Something that is hard to do if you're playing silly buggers with another nation's boomer. So we'd be talking serious dereliction of duty on the part of the captains, which I judge rather unlikely. No nation will leave the keys to their only boomer in the hands of an irresponsible idiot.
*) Unless, of course, the boomer in question is a Russian Typhoon. Their job is to be always ready to destroy a LARGE country at a moment's notice. Can you imagine 200 warheads each of 200kT** yield? That's gonna leave a mark!
**) More than 10 Hiroshima-sized bombs (13-18kT)
3) Men have died under these circumstances before. As noted in the article, collisions were relatively common during the Cold War. I've read about one such incident where the Soviet sub struck the American sub's sail with its prop. The prop-shaft was bent so far out of shape that the water-seal ruptured. The sub filled up so quickly that there wasn't time to seal the bulkheads, and she imploded just a few minutes later.
(Obviously these details had to be inferred from the damage to the American sub, and the recordings of that sub's passive sonar. No-one on the Soviet sub survived, and I doubt anyone ever even found the wreckage.)