FASA never said they were Fed Members, quite the opposite in fact. In FASA the Orions controlled a small volume of space near the Klingon border and "traded" (smuggled, pirated, etc. etc.) throughout most of known space.
In the Star Fleet Universe (Star Fleet Battles, Federation and Empire, Prime Directive games plus some of the background for the computer game Star Fleet Command) they were Federation members but had a clause in their membership treaty that allowed them to remain neutral during the General War.
In both the FASA and SFU versions the pirates may or may not be under the orders of the Orion government. Few people know and those who do know won't say.
Being surrounded by the Federation but staying independent could be a very attractive proposition. You're protected from, e.g. Romulan, invasion by the surrounding Federation territory but you don't have to toe the line with regards to Federation taxes, laws, morality, etc.
"And all I ask is a tall ship, and a star to steer her by."
"Though a cloaking device, pulsed phaser cannons
and a full load of quantum torpedoes would be quite nice too."