How would the US react to the same request from EU's police? Would they give direct access to their people's biometric data? Conversely, what would the EU do if that same request came from another nation instead of the USA? What about Brazil, Japan, China?
Given the US has army bases all in and around Europe, more than any European country, I bet the US wouldn't comply. It's rarely talked about, but you gotta imagine, the fact the US controls most of the land and sea is a big factor in how diplomatic issues are resolved. I don't think this is a great thing, btw.
In the 80s USA sent troops in italy to kidnap a terrorist that had surrendered himself to italy. They had to call up all the available carabinieri on the island to counter the USA troops.
Not one has in mind with "allied nation".