So by the rules I can have two Dr. Doom's on my team as long as one is the Secret Invasion version and the other is the Classics version. The rule book states:

Unique characters. A force can contain more than one of the
same character. However, if a character’s rank is Unique, it can appear in
your force only once. Unique characters have silver, bronze, or gold rings
on their bases. Two Unique characters with the same name, set symbol, and
collector’s number can’t be on the same force; however, a Unique character
can be part of a force with non-Unique characters that share the same
name, as well as with Unique characters that have the same name but a
different collector’s number or set symbol.

Am I right in this assessment?

You are correct. The Fantastic Four starter Dr. Doom is a different figure by name, set, and number, so even though it is Unique, you could play one of each on your team.

This first became an issue when the Universe set came out; there were Uniques in both that you could play twice on your teams, if you had them.

you got it right.

I'm glad you posted this, 'Rager. I was just coming on here to post it for confirmation. I'd never actually seen anyone do that in the Universe-print era, so I didn't know if there was some bizarre stipulation about it.

Hmmm, have to keep that in mind during the next 600 event...