Tabloids toe the line more so than other publications.
They would never publish classified material without clearing it first with the UK government. And at minimum carefully redacting information that would put people in harm's way.
There seems to be a hypothesis nestled in there that the tabloids are run by responsible, clear thinking individuals who are pretending to be uncivilised boors but will drop the facade when confronted with an important issue.
What odds might be put on them actual being uncivilised boors who'll publish anything that gets eyeballs?
More likely they wouldn't publish raw classified information because it is dry and boring.
No, it's the "just a blogger" thing - if you only publish on the internet and not in print then your journalistic credentials will always be slightly suspect.
(source: I ran a newspaper, and while 90% of our readers read our stories on our website or FB page, according to our market research the fact that we printed actual paper gave us way more credibility with our audience than competitors who just published on the internet)