Not to say their statement is true but I don't see any reason to count the initial zeroes.

11100 == 111 == 11100000000, in terms of the next odd iteration

Even numbers don't really count in the process surely? All collatz does is essentially ignore those zeroes

Valid point: it depends what invariants you're trying to construct. Considering only the odd elements of the sequence does yield a slightly different set of insights compared to other approaches. (9 / 28 / 52 still describe a counterexample to the proposed invariant, even in this scheme.)