It's sort of almost correct. He's fumbling his way towards the avalanche property: for a perfect cryptographic hash if you flip a single bit in the input, on average half the bits in the output will change.
Yes, but the Avalanche effect does not mean it is not invertible. It is possible to design a one way hash function with remarkable avalanche (50% of flipped bits on average after 1 bit change in input) effect but that is easily invertible.
The simplest would be an hash function that outputs an N-bit hash where M bits are a pseudo-random sequence of bits (depending on the input, let's say SHA1(input)) that are used to key a stream cipher, and the rest N-M bits are the XOR between the stream cipher output and part of the input of the hash function.
Perfect Avalanche effect, but the function is invertible.
An hash function is invertible enough if it will leak the first three bytes of the input. Does not need to be invertible as F^-1 in mathematical notation.
http://en.wikipedia.org/wiki/Avalanche_effect