I've heard of this also but have not done the soaking in the tub method.
I do use a very damp cloth to wipe down the surface of my cutting mat, getting out all the bits of lint that get into the cutting 'tracks' ... it seems to heal very well when I do this. My cutting mat is newer, got it last year, and did not want it to get as damaged as my old one that I had for probably 8-9 yrs.
One day I will do the soak-in-the-tub method.