Nature is exactly that, what happens naturally. What it isn't is a name for trees and habitats and birds and bees and what we know to be.
When we introduced the grey squirrel, things changed and then found an equilibrium again, naturally. It's what nature does best! That this natural occurrance displeases people will only force them away from nature.
To presume we aren't a part of nature and therefore must act outside of nature to (and this is the really perverse part) 'help' nature automatically precludes our exclusion from nature. But that is a paradox, because we are here, a part of nature. Another 'over'-populated creature on this planet. Well, our overpopulation is inevitably our problem, so eventually that will find its natural path too, along with the squirrels. Playing big brother in the attempt to 'vote out' mr grey is ultimately missing the real benefit of being a part of nature. Our total emersion within it.
If you didn't manage to pass safely through those last two convoluted paragraphs, suffice it to say, be a predator if you will but why play god on behalf of nature?
I voted that I watch them, simply because I prefer to eat other food and because I've never needed to hunt (or protect my bird feeder
).