So what is the concern here? The USA wants to check those who turn up at their border is who they say they are, and they also want to know if they are a good egg as far as the authorities know where they are from. Both of these sound iminently reasonable.
What they probably want is getting fingerprints for a specific person in automated way. Getting fingerprints per police request is kinda reasonable, but as far as I remember, European law on this stuff limits gathering biometrics for a specific reason -- document issuance. I doubt even police of the same European country would have automated unrestricted access to this database for investigation purposes.
For identification purposes and when permitted by a judge -- maybe.