I think the clue to the real reason of the decline in population is included in the article:
Already suffering from a loss of their favoured woodlands, red squirrel numbers have plummeted
Red squirrels suffer next to their grey cousins because they are more picky about what they eat, are more picky about where they live, they have less young, and are less able to survive severe winters. Parapox virus, the thing that some grey squirrels carry, (along with Cattle, sheep and goats) is not the Red killer it’s sometimes painted to be, and Red are developing an immunity to it. Recent autopsies performed on red squirrels have revealed Parapox antibodies (meaning they got it, and recovered)
The real killer of the Red squirrel population is mostly us.
All the stuff about greys being rats, and so on, is just so much propaganda.