I only decided to provide my ID docs just before I decided that I wanted to get a fiat withdraw underway. It was a big deal to me as I value such docs highly.
Mt. Gox rejected my docs initially also for a bogus reason: My P.O. box appeared on my driver's license along with my physical address since it is common for people in my area to avoid their street mailbox due to theft and vandalism. After a rather frustrated note, they went ahead and verified me. By that time I was pissed because I had already sent them my docs and the damage was done.
If Mt. Gox would have been honest and said that they simply cannot send funds to U.S. customers via intl wire and don't know when they will be able to, I would have chosen to not sacrifice my identity documents. I am rather pissed at them because their deceit cost me the loss of my docs and I value them at upwards of $10k.
In my case I have never had any trouble taking BTC out. I took out around 50 in Aug before I verified and made a sale of another 50. I took out my last 5 a week or two ago since I figure there is a good chance that Mt. Gox will totally fold, and even if they do not, I see little reason to attempt to do further business with them unless I am very desperate.
My best guess from experience and research is that Mt. Gox hassles people for ID docs on BTC withdraws mostly when they have significant concerns about fraud or criminality on the part of the user.
Yeah they gave me some BS line too when I sent some documents in, including a scan of my passport. They said my proof of residency was unacceptable. I argued with them and they said they would consider a W-2 form from last year. However, I'm not too sure I want to trust them with it as it has my SSN on it.