Changed my rear tire a couple months ago and did not use straps. Just be careful and use common sense. Jack will hold bike. here's a picture while tire was off bike.
You do not need straps, I have one of these and it is a great product. Last week I was sitting on the bike while it was on the jack checking the highway foot peg position. Justy follow instructions correctly and make sure the jack is locked in below. Go to the website if you are not sure.
I have a 2011 street glide and a j&s Jack although straps are the best security I have never strapped my bike it is steady as a rock I push it all over the shop and have never felt it would fall but as i know I will get slammed on this make sure you strap yours........
Never used tiedowns with my S&S Jack. It is most stable when raised fully for some reason. Plenty stable at all heights. Have used it with a Goldwing gl1800 also and changed rear wheel with confidence, steady as a rock.
I would place something under the front wheel before removing the rear one.. You may not need to, but it's supper cheap insurance to keep the bike from tipping over if/when the weight distribution on the jack suddenly changes.
I've had my rear wheel (and/or front) off the bike with my J&S many times and have never used straps. Like was said before, there is a lot of difference between the J&S or Pitbull and a $75 narrow Chinese jack.