bet/fold vs check/call on the river

[meanjean]

I've been hanging in the HUSH forum for a while and it appears that many people seem to advocate the bet fold method when a scare card falls on the river. For example, the third to the flush or something that pairs the board. I see this as wrong in most cases but am willing to be corrected. Is anybody willing to give a good example of when a bet/fold is correct on the river? Something clear cut.

Thanks, I'm just trying to "get" the logic behind the bet/fold concept as compared to check call.