2) If they did, why didn't those documenting the songs at the time spot that these songs were really Urban products?

There are lots of possible answers to this and others will probably add to my list.
Most of the collectors were not particularly interested in their origins. Presumably they were happy to accept Sharp's doctrine. Baring Gould and Kidson aside, few of them had done any research on this and we already know that they were much more interested in the tunes. Vaughan Williams frequently didn't even bother to note any more than the first verse of the text. As stated baring Gould and Kidson were well aware of the broadside influence but they lived far away from London where all the organising went on under Sharp's watchful eye.