Browning makes some nice precision rifles, like the M1000 Eclipse, and as for out of the box accuracy they are probably as good as anything I can think of in North America, except they are a Browning design. The lugs scare off some people since they percieve them to be harder to work on than something more simple like a 2 lug gun, as well you will hear some complaints about the barrels in them being hard to get out, but ultimately in my experience, thier price, and craptacular magazines put them out of contention. If you are working on the basis of buying a gun, then overhauling it, the Brownings are an expensive starting point, stock options are limited until now (some nice ones showing up). For the price point you will be in, most people would just go to a higher end rifle and call it a day. Lastly the magazines are shi*. Thier mags are a good hunting rifle design but blow at everything else. Using them from a bench or prone requires three hands, and thats where I left them, for example.
For years the only 'precision-ish' rig that Browning had was the m1000 in 300wm, they have slowly opened thier line up, with that I think you will see more of them creeping in, but it will be Browning owners driving it, dont expect builders or suppliers to rush to them.