Fun tidbit....when you check the 'I'm not a robot box', what you are doing is signing an agreement that the website can scan your browser history and see if it looks like the history of a human rather than a bot. This is RAPIDLY becoming useless.
My first thought: I'm not sure that is true. If they can see my browsing history (as opposed to my browser history), it is likely through other means, and not through access to my browser or through any permission I give it.
What they can see, for example: I know each web page is provided the address a viewer is coming from, and where the viewer is going to. So, for example, if I come here from Youtube, and go from this page to CNN directly (e.g., by clicking a CNN favorite/bookmark), then this site can see that I went to CNN when I leave. But, if I open a new tab and go there, this site cannot see that. Google, Amazon, etc. have ads on web pages all over the Internet, and when I go to CNN, for example, the google ad will let google know that a computer with a particular IP address visited homesteadingforum.org (if google has an ad here) and cnn.com (if google has an ad there). When I later go log in to google to check my gmail (or go login to youtube), then google will have a much better way to identify me, as they will then be able to tie my IP address to that gmail account and/or youtube account (with the browsing history there that they kept). If I then go login at Amazon, they can do the same thing.
But, I don't think a simple check of that box does all that much, though.
My second thought: If I am wrong, and it is true that I give access to my browser history, then it is a good thing for me that my entire browser history is deleted every time I close my browser. All they will get is what I did in that particular session.
My third thought: If it is true, then that means that outsiders have much better access to my browser than I think they do. I use FireFox, so at least the code for that browser is available to the public, and hopefully someone would notice such a gaping security hole. Not sure if Edge or Chrome are as transparent. And, since Chrome is a Google product, it may report more on us to Google than Firefox will.