I can definitely attest to the fact that they will cross/swim a river. I used to hunt just off the edge of a river as the does and yearlings would cross the bridge every morning and every evening. The bucks swam the river 10-80 yards downwind. The bucks never used the bridge.
Never shot one there as some guy claimed that the crown land was his and insisted on standing and talking/threatening/yelling at me while I was in my stand. I don't hunt there anymore, as I took my stand down that morning and haven't been back. I hunt for the peace and quiet, not to hang around idiots. I could stay in the city for that...