I would consider that fact as having the exact opposite meaning. The disciples, finding the burial clothes lying empty in the tomb, were more concerned with the question of where the body had gone. It was several hours yet before they saw Jesus alive, and after that, they forgot all about the tomb and everything in it.
In fact, the tomb itself was lost for years, because, as an empty hole, it was simply not sufficiently interesting to be marked. It was just a place where Jesus had spent a few hours, like so many others.
Ah, you forget Mary Magdalen was there too. She was a woman who loved Our Lord very much. I doubt she forgot about anything that had touched His body. She and her friends probably gathered up the linen keepsakes out of love and reverence. It’s something women do.
Feeling as they all did about Christ, after having heard His words about His blood, they probably regarded the burial linens with His blood all over them as sacred from the very first moments.