We met up with him at the pub.

It has the same meaning as bumped into and therefore can be used with people you already know.

They are meeting secretly every Wednesday.

You could say they are seeing each other secretly, but to me this sounds clumsy.

The list of examples could go on but I think meet/met can be used with people you know but only in some circumstances.

I think used as a greeting it should be nice to see you after you know the person

For someone you already know, the only time “meet” would be used regards time and/or location, i.e., “I’ll meet you tomorrow at 2 at the café.” For someone you know only by email/phone,

you could say “I’m looking forward to meeting you in person.”