<<The US have no access to our criminal database>>
That's not the issue though - the guy who checks your passport won't have access, sure. He WILL though have a list of passports/people the US are 'interested' in which will include input from us of passports/people WE are 'interested' in. What prompts inclusion in that list I've no idea.
But his boss - or his bosses boss, or his boss, will by going through the right channels, be able to find out anything they like about you, maybe not by directly interrogating the database, but by asking the right person here.
And if you arouse enough suspicion when you arrive, they are going to ask.