I am sure I have heard so too but i do not know of any scientific evidence to support it.
I suppose getting old in this scenario means wrinkling of the skin?
Your skin cells get replaced every 2-3 weeks. As you get older, the rate at which these replacement takes place might decrease which might result in older looking skin in old people. Wrinkling on the other hand I think is a factor of the muscles under your skin getting wasted. I suspect that this too might have a link with how fast cells are replaced in old age.
Hot water might cause scalding…aging? I do not know