What does "check out" mean in this context? I can't get it. Thanks for your help.

Producer - Good, thanks. A lot of it checks out.
Man - Her?
Producer -Right. Ms. Donovan, if you don't mind, we'd like to put you on.
Ms. Donovan - That's why I'm here.
Producer - All right, great. Holly here will be asking the questions. Just watch his hand, okay?
Reporter - Evening, Peter. I'm with Veronica Donovan, the lawyer for Lincoln Burrows. You're petitioning for a stay, is that right?
Ms. Donovan - That's right.

It means that it matches what is expected of it.
Or that a claim someone has made or story he's told can be independently verified.
Students: We have free audio pronunciation exercises.
To "check something out" is to verify or investigate it. So something that "checks out" has been investigated and at least found to plausible, believable, with no glaring flaws, and supported by some evidence. It doesn't generally imply a thorough or painstaking investigation.
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