I don't understand the logic of this rule.
[238.5.2] Breakthrough Advance: .... A Breakthrough Advance is not Movement, per se; Advancing units spend no Movement Points, pay no terrain costs, and can move directly from one EZOC to another across Major River and Strait hexsides (i.e. it can grab a bridgehead; see 211.1).
I have a solidly manned major river line, but happen to have a few weak stragglers on the wrong side of the river. Why does a breakthrough give the enemy a free river crossing (bridgehead)? It doesn't make logic sense to me.
The rule didn't have to be this way, but reflects confusion that a BT can have on other defenders. It can look odd at times, but rules can often have odd-looking effects now and then..
It won't if you have a unit-in-every-hex-across-the-river. However, if you don't, and there is a gap between units across the river, a Breakthrough advance can enter that gap space in your river defense coverage.