Coloured Stamps

Jody’s stamps are one red and one yellow.  As you don’t need to know, Steve had two red stamps, and Jody reasoned:

“If any two of us had four stamps of the same colour between us, the other could easily have worked it out the first time round.  Further, since Steve and I didn’t know ours at first, then by this very logic, if I had two yellow stamps Ian would have been able to work out that his was one of each colour.  But he didn’t, so mine is clearly neither two reds nor two yellows. So I’ve got one of each.”

The same argument would apply if Steve’s stamps had been both yellow; a similar thought process would reveal the same result if Steve had one of each.

Did you solve it this way?  Or did you realise that, since the problem is symmetric in red and yellow, a unique solution must be too?