Let's start with...
That's not Nick Fury and Maria Hill...as we later find out it's actually Talos and Soren who are Skrulls masquerading as them.
Talos even says at the end of the movie
Come on, Soren, how was I supposed to know the whole thing was fake? I mean, that was all very, very convincing, you know. The performances, the illusion, that costume, the craftsmanship in that. I mean, this is just embarrassing for a shape-shifter.
Clearly they were taken in by Beck's story and, as has been said elsewhere...even if they did use their information sources (not SHIELD's apparently) all that would do is confirm that Mysterio looks like Quentin Beck.
But that in itself means nothing since he never denies being Quentin Beck...he's just a different Quentin Beck from another universe.
The fact that the supposed "real" Beck is a hologram expert doesn't necessarily mean that they should be suspicious since holograms can't affect physical objects.
They aren't to know that Beck has actually assembled a team to fake the disasters...
The integration of my illusion tech, with your weaponized drones, was brilliant. Powerful illusions, real damage, worked like a charm. And it's just the beginning.
Staging electromagnetic pulses at each attack site so Fury's own satellites would confirm our lies? Inspired idea. To Janice!