I stopped at a Walmart in Texas, because we needed to get to a local tire shop first thing in the morning and the Walmart was close. I went in and asked the manager if we could stop for about 6 hours. He had to think about it for quite a while and finally said OK, after a few questions. By morning, there were quite a number of vehicles and big rigs there. People sleeping and I'm sure they didn't all go ask as I did.
I find the truck stops, like Flying J, Love's, etc, to be much easier and less of a concern. They expect a hundred trucks every night and they don't even notice a trailer or two. We get tucked in, out of the way, and never have any problems. They often have a McDonalds next to them, for morning coffee, etc.
One night, in Kanab Utah, I asked a police officer if there was a spot I could stop and rest for a while. He immediately directed my to the Wendy's restaurant. It had a big lot and there were a few people there with big rigs, motorhomes and travel trailers. Perfect.
Out west, there are a lot of spots to stop as needed, and I have never been confronted. The only time I had an indignant response to my asking, was at an old Nevada 1950s style casino/hotel. When I asked, the proprietor could not figure out why I was asking. He finally pointed out that "people often come and stay in our parking lot for a couple of weeks". "Of course you can stop for the night, that's what it's for!" I thanked him and have been back over and over on our way through. I never ask and I feel perfectly comfortable there. Sometimes for a couple of nights.
I only exaggerate enough to compensate for being taken with a grain of salt.