Is it OK to contact movie production companies once we've exhausted the agent possibilities?

That's the circle, though. It's easier to get sold if you have an agent. It's easier to get an agent if you've sold.

Typically, I've always heard it's an extreme long shot to go to production companies directly, but I did go against that conventional wisdom and get a bit of a payoff. I contacted a smaller, independent film company exec via phone and just gave an over the phone query. He said he'd read my stuff eventually if I sent it, and he did. I heard back I believe the next day, and he was asking for more. I work as a freelance writer off and on with that company. It's great, but I have to stress, THIS IS THE EXCEPTION AND NOT THE RULE.

Maybe you can network small first and build your way up. Alternatively competitions and conferences are great places to be seen by agents and even some companies. You may have better luck there.

In most cases, a legit Prod. Co. and the like won't touch an unrepped MS unless you've got an existing connection. And by "won't touch," I mean, "delete on receipt."

It's a protective measure against lawsuits in the event that their new blockbuster happens to run similar lines (or not so similar, if the writer is paranoid) to something they're sent. To stop the lawsuits, emails from unknown accounts, or those with specific words in the titles go to a folder for deletion. Sometimes, you'll even get a note back from the legal department that's automatically generated by the email's presence in the delete file.

The link appears to refer to book manuscripts and not screenplays.

It's fine to query prodcos (big and small), agents and managers with a screenplay logline. I've had plenty of script requests from all three, although I'm not repped yet!

If you do get a producer interested, certainly try to find an agent to negotiate on your behalf.