Legal Question in Real Estate Law in California

Yes, The bank is under no obligation to sell to you, or anyone else, and can heap all kinds of conditions on its counter-offer. There is perhaps some advantage to the bank in imposing such a condition -- it can control the approval and granting process and there will be no unexpected last-minute hangups with the loan falling through. Just be glad they aren't requiring you to move your checking accounts as well.

If their loan terms are competitive, this may be an advantage to you, as well.

Or, you can counter-counter offer.

Of course.