Sources with direct knowledge tell TMZ that reports suggesting Matt was left high and dry during the first night of his 3-night stand-up show at NYC's legendary Radio City Music Hall this past weekend are simply false ... although, we know Pete did not, in fact, perform.

There's a perfectly good reason, though ... our sources tell us PD was never technically contracted or scheduled to get on stage as an opener ... but we're told he was asked.

Here's what actually unfolded ... our sources say Matt extended an invite to Pete for his show, and while we're told the ex-'SNL'er would've loved to come and cheer on his pal -- our sources tell us he simply couldn't make it ... and he even told Matt directly.

On the face of it ... there seems to have been a misunderstanding/miscommunication between Matt and his own team ... that's what we're being told anyway. Pete relayed the message.

Our sources also add this ... Pete has nothing but love for Matt, but he couldn't make the show because he was already booked and busy with gigs of his own.

Pete had a stand-up show on Feb. 4, meaning he had to travel Feb. 3 to make it there -- both dates falling on Matt's shows in NYC. In addition to being in the middle of his own stand-up tour ... we're told Pete's also starting production on a film with Eddie Murphy.

So the big news here is that there really isn't any news at all. That's not to say Matt's performances lately haven't been eventful ... 'cause they certainly have.

Remember, porn star Lisa Ann was cuffed and dragged outta Matt's show for allegedly acting "drunk and disorderly," according to cops. Now, that was quite the dramatic scene.