If the compression was low in that jug... (From rusty rings) then yes.... that can cause it to stick. Basically, once the rings stop sealing... the hot blow-by gasses will over heat the skirt, and displace oil. A "Low compression" melt down will normally look like lack of oil. BUT... the answer lies in the crank bearings. If they are wet with oil... the injection was working.
One other thing... if you had a case leak... or a crank leak (bad seal) then that will cause that jug to go lean.