Gmail – Is it a good idea to mark Facebook spam notifications as spam in Gmail

I set up Facebook to email me notifications to Gmail whenever someone sends me a message. The problem is that I have been getting spam messages from people I don't even know. What's interesting is that 100% of these notifications were sent to my spam folder in Gmail. I'm guessing that this happened because these same spammers sent messages to other Gmail users and those users marked the messages as spam. Or it might be because of the content of the messages which looks spammy.

Ideally I would prefer not to be bothered with these spam messages in Gmail and only have to deal with them from within Facebook when I log on, so Gmail recognizing them as spam is a good thing.

The problem is that I found a false positive. That is, a real friend of mine sent me a message and it appeared in the spam folder.

I'm wondering if I should I keep these messages in the spam folder or not. I'm afraid that if I keep them in the spam folder, this will contribute to getting more false positives, since the subject line is very similar ([friend] sent you a message).

Is allowing Gmail to filter out some of these messages even a good idea? Shouldn't it just take all the messages from Facebook and present them to me, and it should be Facebook's job to filter the spam?

The problem with this last scenario, though, is that I'm also afraid that if I don't mark these messages as spam, I will get spammy content in messages marked as not spam, thus messing up my spam filter even further.

What do you think?

Side note: I've tried marking messages from Facebook as spam, but it didn't help reducing the amount of spam I get at all.