Here is proof, brought to my attention by a biographer of Jane Jacobs, Professor Peter Laurence.
The picture below is of her riding her bike on what appears to be Washington Street, just north of Canal Street. She is riding in the direction of what is now Tribeca. Note that the entire area there is now unrecognizable. It has been taken over by new modern buildings, with more to come as Trinity redevelops that area with their awful redevelopment plan. I don’t think the two federal houses on the left are there anymore, alas (but maybe I am wrong).
So man up, bike lobby! If Jane Jacobs can ride her bike on cobblestones, you can too.