Because of the nature of nuclear secrecy, we'll probably never know the rest of the story...but my guess is, it isn't as much of an "accident" as we're being told. Submarines track and shadow one another all the time. The sub being following can't easily detect another sub directly behind it because of the sounds of it's own screws. The following sub would be using passive sonar only, meaning it's only listening, but not "pinging" for targets.
The term "Crazy Ivan" came from the days that Soviet sub drivers would often change course abruptly or even reverse their screws in order to get any submarines following them to have to evade a collision, and therefore, bring them into an attitude where the Soviet sonar could detect them. This collision could very well be the result of one or the other "pulling a Crazy Ivan".
What would be interesting about the rest of the story would be, why would a French or British submarine be shadowing the other?