I also don't like rubber-backed. They tend to disintegrate. At best, it makes a mess when it decays. At worst, it melts into both your floor and rug, like old chewing gum, and causes permanent damage.

Personally, I also wouldn't sew anything to the rug. If it's a big rug, it will stay in place. If it's a small rug, go to a really respected (not necessarily expensive) rug store that sells old rugs and ask what they recommend, then cut pieces smaller than the rug if the stuff is thin, EXACTLY the size of the rug if it's thick (to prevent the threads breaking).

The rubber also stinks!

watch out

I installed a soild oak plank floor about 9 years ago. Tounge and groove. A life time finish from Armstrong. It has held up beautifully in the traffic areas.

On the other hand we acquired two dogs 5 years ago. i put a 3 x3 piece of carpet down for their water bowls as they slipped on the wood.

Some how the carpet got wet over a period of time.

One morning i came in and a 4x6 area had severly buckled. The carpet was damp. The nails i used were rusted so i knew it didn't happen over night. I real choir to repair, especially since the color had been discontinued

I know nothing about Brazilian cherry. We put oak in about a year a go and we have 2 area rugs. The one in the prep area of the kitchen is an inexpensive 8x10 from Bed Bath and Beyond. It has a rubber backing. So far so good. It was chosen for it's ability to camouflage tomato sauce and catch drips of both fat from the stove and water from the sink and dishwasher. When it starts to disintegrate it will be replaced by another one. No problems so far and I look under it occasionally. In the sunroom we have a wool rug. The floor is doing fine with it too. I hope to keep it longer than the kitchen one as it is more expensive and more of a decorative item.

The only things I know about rugs are that if they are very small you better either have a rubber backing or a non slip mat under it or someone is going to get hurt on it. Secondly if you have a new light wood like cherry the part you cover will stay light while the rest of the floor colors naturally with age. If you then remove that rug the floor areas won't match in color. Same if you cover it with anything as the exposure to light colors it.

I wouldn't stress too much. Wood is very durable and a natural flooring material, just remember it's a floor not a coffee table.

I would not use rubber back rugs on hardwood. There are application specific cushions, and non-slip membranes, that will not harm the surface/finish.

Be aware... The rugs covering the wood, will not let UV light to that wood under there. The flooring around the rugs or furniture is going to darken and when you move furniture and rugs, it will be obviously lighter in color. Move rugs and furniture often for the first year, to let the floor patina evenly.

I dont use any padding etc for my woolen handknotted oriental rugs. Just sit on the hardwood as well as stone floors. They dont move around.
We take up the rugs during the summer. This lets the wood patina evenly although I havent noticed much difference in color in the darker wood floor. The indonesian cherry did darken unevenly but a couple of weeks of no rugs fixed it.