The impression I got the other day at the First Wing was that the default position is to deny boarding and then only allow once the passenger presents their case that they are permitted entry to wherever they’re trying to get to.
We were told we wouldn’t be able to travel to Gibraltar and we’d need to go and get tests (before the announcement the other day). The agent was having none of it until I politely requested they check Timatic and that it is test on arrival. Still, after consulting Timatic, they needed 2 telephone calls before they pressed print on our BPs.
A US citizen at the next desk was having similar issues despite having print outs of the rules of his intended EU destination.