Really theres nothing RunUO will have to worry about. In order for PunkBuster to do all these things, you will have to agree to their TOS. If you don't hit the "I agree" button, it will not install. Also like someone else said, EA is having a non-PunkBuster server. That means if you don't have to install it to play an official server, you won't have to have it installed to use the client itself.
Also for all the privacy freaks, PunkBuster's license agreement specifically states (an entire paragraph devoted to this one point) that everything it does is done to stop cheat programs and software. That means if they take your personal information and do something with it not involving cheat detection, they are in breach of their own contract and you can sue them for the big bucks. By stating that they can look at your harddrive and take screenshots, does not mean they can use the information for anything else besides what they stated in the agreement. Also note that there aren't employees scanning harddrives, its a machine that does the scans. Machines can't read, it will scan for cheats and then send a report to whoever requested the scan with a few system specifications and whether it found cheats or not.
As for the global bans, PunkBuster has stated that they will not handle the bans. On official servers, if a cheat is detected on your system it will alert a GM who will take the apropriate actions.
But if you only play RunUO you don't have to worry about any of this since as long as you dont hit the "I agree" button on their terms of service, they can't do anything. And as I said, I doubt you will have to have PunkBuster active to use the client since there will be non-PunkBuster servers.
Whew.... Anymore questions? Hehe.