I’ve never heard that and it may be true.. however, everything I’ve read recommends hot water for a good, close shave. Even if you put a washcloth under hot water and hold it against your face for a bit is helpful. The reason is the hot water causes the pores to open and the hairs to expand, giving you a closer shave (you can attack more of the individual hairs that way). Keeping the razor blade hot while shaving helps in this department, too.
When women are given advice about shaving their ladybits, they always say to sit in a hot bath, use a sharp, new-ish razor, keep the razor hot, and use some sort of skin lubricant (shaving cream or gel). Seems to work pretty well.