The data on the left hand side of the myheritage screen is simply being echoed back to you in the browser so that you can see your data plus the data that actually is in myheritage on the same screen without having to flip back and forth between RM and the browser. It's not really "in myheritage" in the sense that other users can see it. You cannot turn off this echo except by turning of the WebHints for myheritage entirely.
The stuff on the right hand of the screen is basically available for all to see, whether you ever use RM or not, whether you ever use myheritage or not, or whether you ever use the Internet or not. It's extracted from numerous and diverse public domain sources such as marriage records, divorce records, tax records, phone directories, and the like. Actual birth and death certificates are not generally speaking in the public domain in most locales, but a tremendous amount of other information is in the public domain.
If you really don't want to see all that stuff, then just turn off the WebHints for MyHeritage. The data will still be there, but you won't see it so you may feel better about it. I'm reminded of a well known saying that's taught to student pilots when they are getting their license. It has to do with flying at night in a small aircraft. If you have an engine failure at night, when you get close to the ground then turn on your landing light. If you don't like what you see, turn the landing light off.
Thank you Jerry. I think I understand it a little better now. Your explanations are very clear. I am not used to all of the features of RM 7 but am slowly learning. I appreciate your help. I am amazed at all of the information that is out there on the net.