I always stretch my strings. I don't know what the YT vid is recommending (can't do YT @ work, but I can do TB

), but I fret the new string at the 1st fret, then grab the new string with my right hand at the 12th fret and tug on it repeatedly (not too hard, just a little tug). Then, I retune and do it again until the string stops stretching. It usually only takes 1-2 minutes per string and my strings hardly ever go out of tune after this is done. I've done this for years on both bass and guitar and it doesn't hurt anything if you do it right.