I have been playing under the impression that major rivers prevented corps/army from MTSGing in support of another unit. In previous games, on three separate occasions I've had a corps/army on one side of a major river and another corps on the other bank that didn't MTSG. I'd pretty much taken it as a given that corps on opposite sides of a major river didn't provide mutual support. But I just had an occasion in a current game where a corps MTSG'd to an army stack that came under attack despite being on the other side of a major river.
In this occasion, there was a rail line that connected both regions. But that was true once in the past as well. And on two occasions I checked to see how long it would take for either stack to march to the other and the weather was clear with no mud or anything else to slow down movement. So how exactly does a major river influence a corps chances to MTSG? Did I just get unlucky in the past or did I get lucky this time around?