On many of the older pumps if you kept the trigger depressed as you were working the action the gun would fire as soon as the next round was chambered and the bolt closed. They were designed this way on purpose. I had more than one old timer tell me that a pump was unsafe and they would not own one because of this. They did not realise that none of the modern guns would do this. This may have been what he was refering to.
If a gun has worn parts it could fire. I know of one case where an old worn out single shot was kept loaded under a bed that fired on its own during the night under the bed. When checked by a gunsmith it was discovered that there was so little metal between the sear and trigger that they suspected that on the cold winter night the metal contracted enough to let the gun fire.