i get what youre saying with the diagram, but i still dont agree with it. not saying that im right, but heres my thought process.
yes, there are 4 possible outcomes if you flip 2 coins (hh, tt, ht, th). however, if your friend looks and sees that one of them is tails, it would rule out two possibilities. obviously, it rules out hh, because one is tails...but it would it also rule out either ht or th.
pretend instead of two identical coins, you had two different coins, like a quarter and a nickel. you still start with the same 4 possibilities, but you can lay them out differently (quarter:heads nickel:heads, quarter:heads nickel:tails, quarter:tails nickel:heads, quarter:tails nickel:tails). in the case, when your friend looks under the table, he will not only see that one of the coins is tails, but also which coin it is. for example, if he saw that the quarter was tails, it would eliminate both options in which the quarter was tails, and only leave the two options where it wasnt.
it seems (to me, anyway) that the same principle would apply to any two coins, regardless of whether or not they were the same.