Not sure if you been asked this, but didn’t Theon knelt before Robb proclaiming him “King in the North” along with the North and Riverland lords? Doesn’t that make the Iron Islands part of Robb’s Kingdom just like Edmure kneeling while his father was alive did? Even if that wasn’t the case, and Balon can reject it doesn’t that still mean Theon is still a vassal of Robb? Is that why Theon is called “Turncloak” or that isn’t the case and he a “Turncloak” because he was a ward of the Starks?

Theon is present during the acclamation ceremony, but isn’t explicitly mentioned as having knelt or pledged his sword. On the other hand, in Catelyn I of ACOK, he does refer to Robb publicly as “the king,” which is suggestive that he did.

Theon’s turncloak status refers to several things: first, he was foster kin to the Starks; second, he fought alongside Robb at the Whispering Woods and the Camps; third he probably did pledge himself personally to Robb at Riverrun.

However, that doesn’t make the Iron Islands part of Robb’s kingdom: unlike in Edmure’s case where he’s in a liminal position because Hoster is clearly on his deathbed but hasn’t died yet, Balon is very much alive and well (just dumb) and is somewhat iffy on Theon inheriting at all; moreover, the Riverlords also bent their knees to Robb, which the lords of the Iron Islands definitely did not.