Yes, that's what it means. They do scan when/if you visit them. I'm not a native, but "is scanning" doesn't sound right here because it means that it's happening right now. However, the title says "the browser" (i.e. the browser of whoever visits) and that is not happening right now, only when that browser does visit. So, I'd say that "is scanning" should go with "browsers" (i.e. they are scanning the browsers in general, not a specific browser).

But anyway, the sentence means what you think it should :).

In general, the working assumption is that this would be limited to LinkedIn's own website, or I suspect this would be a much larger issue ;) The way I interpreted the title is "LinkedIn will do this in the future" rather than "LinkedIn is doing this now if you use their website".