Are you not counting all the 7's in 70, 71, 72, 73, 74, 75, 76, 77, 78, and 79? Or did you miss the ones in 7, 17, 27, 37, 47 etc?
I say 20 also. But it depends how the question are anounced. If he say counts any number 7 then it would be 1, but if he says count any digit 7 then it would be 20.
He also did not specify what number system, if binary 'base 2' the answer is zero 7s (1, 10, 11, 100), if decimal 'base 10' AND counting by whole numbers, IF counting only the number 7 the answer is one, IF counting any digit 7 the answer is twenty, IF not using whole numbers the answer is infinite (1.7, 1.77, 1.777, 1.7777, 2.7, 2.77.........)
Here is one case I would say you were wrong. This is because he did specify. He said: None of us here count in binary, or in integers, we count in whole numbers. He also said: This actually means "how many 7's" It does not specify digits or numbers, just how many 7's. KISS
