King & Rook vs King, Rook, & Pawn
If the pawn is on the 6th, then it depends.
Likely referring to the following game:
You cannot do much with the a or h pawns if the king is in front of it. Even swapping rooks is an easy draw.
You could try putting the rook on the fifth rank and advancing the king to g5 without exchanging pawns at h5, or taking with the king at h5 instead of the pawn. White has a rather easy draw in both cases, but minimal skill is required.
If the pawn is on the 6th, then it depends.
Almost everything in your claim is wrong.
If the opponent king is on the front of the pawn, whatever chances are for a win are associated with the pawn's file. With a pawn at the rook's, or knight's file, even passive defence with the rook on the last rank is sufficient to draw.
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They had a rook and so did I and I ended up in a draw.
Could not figure out how to move everything up.
Help. I think I should have won that game.