"I find it really strange the way “peer-reviewed” is used by the general public as some gold standard of truth."
OK but this member of the general public has at least subscribed to New Scientist since 1987, nine O levels, two A levels, two AS levels and a HND in Civ Eng. All pretty mediocre but I have a fair idea on how sciencing is supposed to work and how it ... actually works. Obviously, I ended up in IT.
I should also point out that maths "peer reviewed" is a bit special. For example Mr Wiles went through quite a maelstrom before his proof of some dodgy marginalia was accepted as "true".