I am assured by people of Reasonable Reputation (I’m looking at you, Chaz) that it is not only okay to re-use not just the jars but the actual lids, even off store-bought jam jars, and that this will not cause the lids to not seal and give everybody botulism and kill them horribly. I am assured of this.
So if the applesauce gives us botulism and kills us horribly, blame Chaz. :)