Not true, you can run the Breen missions early. I had a set that was Mk IV on one toon, early on. When they opened the FEs to everyone, you could do it immediately, pretty much.
Since you can skip missions at will, you can do them whenever you want anyway, and it'll just be at that level. Of course, means that you have to KEEP running those sets of missions if you want to level them up, you don't get one set you can use forever.
Conversely, I was trying to get my KDF character the Borg set before it got harder to achieve (so was running a few STFs to get it quick), and realized I didn't have the console. Of course, she's been a Lvl 50 for a year at least. Dug around and found the mission that awards it to you. The problem? She'd never been to Borg space. Or Breen space. Or Cardassian space. Got Lvl 50 on that character by just playing the KDF-unique missions and then running DOFF missions, I had to skip like 35-40 missions to be allowed to run the Borg one I wanted.
But you can do it, just keep skipping until you get what you need...