Well frankly my dear, the fact that these rags are referred to where you live doesn't say much about where you live.
Not where I live. I don't live in the US. However, the point made was that they were, and are, referred to as tabloids in the northwest US. It appears, from the news articles I linked, that they are referred to as "tabloids" quite widely across the US. Unless, of course, the WSJ, NYT, and Forbes are also in the northwest.
The fact that tabloids exist doesn't mean that anyone with blood supply to the head takes any notice of them. Tabloids can print away. Nobody will care.
Most of these tabloids sell 250,000 units per print run. That's small potatoes, and certainly down from their zenith.
I don't disagree with your premise. The point of this thread was not tabloid influence, but whether they will print articles.
If you've never been in the UK then you may not understand fully what British tabloid culture is, or its reach.
There are a lot of Brits in my city. Anyone I know personally views the tabloids as garbage. Fun to read, just as The Enquirer can be (more so at its zenith in the 1980's), but no one takes it seriously. I'll let the Brits here comment on whether that is their perception in the UK today.
Oh, and incidentally, the Daily Mail's largest traffic is online, and it comes from the US, not the UK.