Might this have been the mixing of two events? The moving of the west elevator (Dougherty) and the arrival of Baker (stairs).
Possibly, I suppose, but it would be quite a mistake for Mr Williams to make (and that's assuming Mr Dougherty's story is legit, which is pretty doubtful IMO!)

Here is Bonnie Ray on his way to City Hall, how old does he look?
Mr Rowland didn't see him on blurry TV footage.
Mr Williams did not look like "an elderly gentleman, bald or practically bald, very thin hair if he wasn't bald"...


And he wasn't wearing a plaid shirt.
Is it possible Mr Rowland got these details badly wrong? Sure. But is it the
likely explanation?