Opinions, please: What is a 1981 Type II Proof Set? Do all coins need to be?

OK, my haste and naivete' may have gotten the better of me once again.
I recently purchased a "1981 Type II Proof Set" from a collector by
mail. I received the set only to discover that all the coins EXCEPT
the SBA were Type II, and the SBA was clearly a Type I.

When I brought this up to the seller, he remarked that the set was
considered Type II if any of the coins were Type II.

I replied to him that since the value of the individual coins appears
to be unevenly weighted, and that the coin with the highest value was
a Type I, the overall valuation of the set should be adjusted
accordingly.

Now, I may have to "eat" this one, and if I do, it will be my
"numismatic tuition" for the year.

My 1979 Type II Set has all 6 coins that are Type II, which I consider
"a set". By my seller's defintion, there could be as many as 6! (6
factorial) or 720 different kinds of Type II sets, each with a
different valuation.

I hope you've been able to stay with me through these ramblings. So
the questions is:

In order for a Type II Proof set to really be "a set", do all 6 coins
need to be Type II.

I'm just trying to determine whether this was my own ignorance (highly
possible), failure to fully disclose the item's condition (possible,
but in my seller's mind, I believe that he believes he was making a
full disclosure), or something in between.

Thanks for your opinions.

DaiLun

P.S. We have requested a definition from the ANA on what constitutes
a Type II "SET", and seller has offered to take the set in and refund
my money.