All police departments have trained techs who fingerprint people who are detained or imprisoned. They are trained and know how to do it properly. They also have the requisite magnetic powder ink and other tools. The have done thousands and I would trust one of them than a private organization.
When I got my fingerprinting done for the FBI PCC, I went to the local police department, they charged me $10. I had to take an appointment and it went flawlessly.
Remember it takes 4 month to get the FBI PCC. In case your card is rejected due to poor prints, or not following doing it properly, you are looking at another 3-4 months. So why risk it, get it right the first time.