Senior Member (>500)
Join Date: Sep 2017
Thanked 25 Times in 24 Posts
All they told you is right. This is a nightmare problem to deal with and there is an extremely high chance of wheel damage if the bold needs to be drilled out, or another method used to extract the bolt. I have a friend who had lug bolts seized on so badly that a shop spent several hours attempting to get it off and were not able to make it budge one bit, and that was a standard lug bolt, not a keyed one.
If you have any mechanical skills, and are willing to spend the time to try to do this right, it might be worth it for you to try the drill the head off method (but again high chance of wheel damage here). Once the head is off, you can at least get the wheel off, or once you are sure the wheel can actually come off and you've drilled the head out, put the wheel back on with only 4 lugs, then take it to a shop to have them extract the stud, probably much easier for them to attempt this with the wheel off and more room, they coul even do some welding to the stud which might make removal easier. It's the drilling of the bolt head and all that cautious stuff that is where the time and money goes.
Good luck and report back once you find a solution!
New (old): 2003 E39 M5 TiAG
Old: 2001 E46 330i Steel-Grey Metallic (Totalled)