Not that I want the wilderness to be compromised, but sometimes old mines and stuff are pretty cool. Maybe the only development we should allow is development that occured 75+ years ago. I'm sure modern mining interests would appreciate that. 
If you are talking about Congressionally designated wilderness areas, when they became wilderness, they were "withdrawn from mineral entry" If there were valid mineral claims when the designation was made, those claims have to be honored. If you are talking about just general public land like National Forests and Bureau of Land Management areas, if there are locatable minerals and someone files a valid claim, they have private property rights to the materials to mine them out. This is under the 1872 mining law as amended.