Nope.. They insisted that I use their company. Their reasoning was that if I used mine, then there would be double the work, because they still had to run it through theirs, in the long run it worked out fine. They actually come out to a mutual meeting place.
I've had banks tell me that I could use my own closing attorney, but that I'd be on the hook to pay the title search and insurance fees (something they normally pay), as they'd be doing that work with their firm anyway...
I have since done some research after posting this and read Section 9 of respa prohibits a seller from requiring the home buyer to use a particular title insurance company, either directly or indirectly, as a condition of sale. Buyers may sue a seller who violates this provision for an amount equal to three times all charges made for the title insurance. Sweet! Here is a link for those who want add'l info.
I agree with Jon. The bank will always set the rules, and they want control of title. They also will not have a problem missing closing dates. That one baffles me, if your buyer is an hour late, all docs need to be rewritten a lot of times. Again bank rules.
Only on rare ocassions have I seen the bank/lender allow buyer to utilize own title company. Like Jon and few others noted, usually lender likes to control entire process.