I'm a 60+ woman living alone in an ultra-safe, bland community. But even if someone said they were LE I would never open the door.
I'd speak to them out the window and call 911 and ask for verification that authentic LE - be it local cops, state, fed, whatever - were on my doorstep. The police station is a mile away and anyone pounding on my door can wait until a squad car arrives to back me up.
I would not open at 2am to a recognized voice unless I could see them, see their vehicle and see that they were unaccompanied. Otherwise, calling 911. Even threat of a gas leak, I'd probably just open a couple of windows till the responders arrived.
And I am lax, hardly paranoid, about security. But there are too many good ruses out there.
As an aside, beware of kittens meowing. Pretending to be an abandoned, scared kitten is one of the eerier ruses used to lure people out of their homes.