It will impact your premium, as your policy underwriter will see a tow claim by listed INSD under 25; I suspect if you had filed the claim (and have a low claim ratio/good scores), the policy ding would be much smaller.
That said, $192 is fairly large tow claim; unless there were significant mitigating issues, I wouldn't authorize payment...it would have to get kicked to an examiner. Typically, the company I work for will reimburse INSD's an average of $60/tow...though there is some wiggle room as we usually work off the bill numbers relayed by the INSD (having them fax it in later). Note: Labor (jump starts, flat tires, lockouts, etc.) is grouped with tow coverages and also runs about $60/hour, with a limit of one hour.
Are you sure State Farm would even reimburse you that much for a tow? You might want to bounce it off your agent, not the 1-800 number you have for claims. If you call it into claims, their CCR's are going to document it as a claim contact (w/claim number), even if you don't proceed for reimbursement. You know who sees that in the file? Underwriters...