While I think it's probably foolish to take any tax advice from anonymous online sources, it's my understanding that the rules of what can be deducted will apply to your business as a whole...and not an individual assignment.
If you are producing income as a shopper and writing off milage, yet showing profit annually, this would seem like a reasonable deduction. If you focus entirely on reimbursement only assignment and use mileage deductions to repeatedly create a loss for your business that allows a significant personal tax deduction, I could see an argument for it being disallowed.
The easy answer is to say, "Consult a tax professional," but I think there is ultimately no black & white rule for allowing deductions. For me, I just like to make sure I have a valid argument for every deduction I take in case it ever comes up. If taking that reimbursement-only assignment can possibly open up the window to better assignment that offer a fee (and with ACL it often will), then there's a good argument for performing the assignment at a loss.