The elk are one both private and public, in this area there is little difference. There are a couple things that cattle operations help, one is all the hay fields and range improvements that you do for cattle benefit the elk as there is more feed and higher quality the second is you need lots of water close for livestock, we try to not have a cow walk over a mile or so to water so you have developed water every where so the wildlife benefits from this also and lets them disperse wider and utilize more feed just as the cattle.
The big rub is Brucellosis, which has been blown out of proportion. There is a very narrow window that the transmission can occur and our elk population hasn't had it so far anyway.
Cattle don't compete for the same feed as hard as say sheep do, and there are only a few thousand sheep left in this county and they have almost zero BLM or forest time, cattle are very hard to get to over graze or even compete for feed because they are so lazy and picky, a sheep band will mow everything down to the roots and you have to be on top of them to keep them moved around.
The ranches are so big here that there is no tall fence so elk move back and forth depending on hunter traffic, feed, and predators. The fencing you see on a normal ranch an elk herd will destroy in one pass, it is no deterrent to them.
I'm not saying everything is perfectly compatible between livestock and wildlife but it isn't like some would have you believe that livestock are the ruin of wildlife, in fact anything that is bad for elk is bad for a cow.