The buying service your credit union uses is similar to the one my credit union uses. I have used their service several times. There is no direct cost to use the service, though the credit union as a whole might have a fee to join the service. I have used it 4 times over the decades.
If you know what make and model you want to purchase, or at least have it narrowed down to just a few choices, you can get an exact price for that make, model, and options. You do this before negotiating a price. You are then issued a certificate. You have to go to a specific salesman at a specific dealership, but near a large city there will be several dealers to pick from.
There is no negotiating at the dealership. You still have to deal with a trade in, and the financing option: dealer, credit union, or cash. But it is nice to not have to negotiate on the price. Of course there is nobody to stop you from using the price from the buying service as a goal when visiting a more conveniently located dealership, that is what I did last time.
The first couple of times I used the standard credit union financing, and the last time I didn't need a loan. Even if you don't use the buying service, one way to pay for the car is to get the loan from the credit union, but get the rebate from the dealer. Many times if you get the low dealer financing you can't get the rebate. Doing it this way actually saves money.
Speaking of rebates see how the buying service addresses them. The big national rebates were still honored during at least one of my purchases. So it turned out to be the buying service price minus $1,000.
If your service worked like my experience, the cost to you was a little time to get the price, and a little time in a different dealer to verify that the price was good.