Why didn't Sidney trust Randy?

First of all, at this point Sydney was really down with her nerves. She had many traumatic experiences in short succession and has just been (and still was) running for her life. So she was in a pretty run down and panicking constitution and I think at this point she didn't trust anyone, no matter if she really had any proper reasons to do so.

Add to this, that she saw Randy just at the edge of being killed by the killer (on the surveillance video), which he then magically wasn't and the fact that Randy in his role as kind of a horror movie nerd always made a good suspect. It is true that Randy sure wasn't the same person that aproached him on the video, but maybe she already took into consideration that it could be more than one (if she even considered so much at all, as written above).

To quote the exchange (from the Scream Script):

RANDY: Jesus, Sid. We gotta get out of here.

Sidney throws the gun forward.

SIDNEY: Stop. Right there.

RANDY: Don't shoot. It's me.

SIDNEY: Don't come any closer.

RANDY: Listen to me, Sid. I found Tatum. She's dead, she's been killed...I think Stu did it.

He takes a step forward when another VOICE SPEAKS UP.

VOICE: Don't believe him, Sid.

Sidney spins around to see Stu moving up the walk.

STU: He's lying. He killed Tatum. And Billy.

Stu moves closer to Sidney.

SIDNEY: Stay away.

She aims the gun in his direction.

STU: His movie nut mind has snapped, Sid. He's gone psycho.

RANDY: Don't listen to him. It's him. He's the one.

STU: Come on, Sid. Give me the gun.

RANDY: No, Sid.

SIDNEY: Fuck you both.

So at this stage in the movie, Sid has witnessed her boyfriend (seemingly!) being killed, Kenny killed, a host of other deaths and terror is gripping her.

Then, in the midst of it, two of her friends, either one of which fits the profile of killer perfectly, show up and tell her to give them her gun. She realises it's a choice between trusting one of them and making the wrong choice or trusting herself and her own instincts. She chooses to do that and shuts them both out of the house, keeping the gun for herself.

Your point is very valid though. She certainly saw the killer in the house. But it's highly unlikely she was thinking logically at this point, given all that had happened.