I thought this was an interesting contention vis a vis the local papers so have gone to the trouble of fact checking it. There are four groups that between them own pretty much all of local media (and a lot of the national stuff too).
Reach plc- listed, no controlling party. You could say that people who own shares in public companies are mainly tories and that may well be true. But not obviously owned by tories. As Mirror Group, this had a left leaning reputation.
Newsquest - listed, but on NYSE. Doubt most investors know what a Tory or a Scotchland is.
DC Thomson - Privately owned, looks like extended family plus maybe some management. Estimate about 80 individuals. Probably some are Tories.
National World- prop David "Rommell" Montgomery. Looks like a Tory. Probably is. Former editor of Mirror though and no obvious political affiliation i could find in a few minutes.
Conclusion - contention not supported by evidence.