Maybe I'm the one who misunderstood the puzzle, but isn't that basically the point? They are trying to trick you into thinking that the rule is "each number must be double the last", when it's actually much simpler. That way, if you don't try numbers that doesn't obey the rule, you won't realize that you've got the wrong theory.

I can't think of any obvious incorrect rule the sequence 2, 4, 7 would fit, so people may have stumbled across the correct answer only by verifying correct sequences.