Yup, Mod Timo confirmed its legit. This is scary but at the same time its bullshit. It is a bluff to scare kids that Jagex will sue them, to stop everyone botting.
Did you purchase from rsbots.net or rsbotting.com? They must have got the paypal emails from one of those sites.
Like I said I haven't even played the game in awhile. I purchased that shit well over a year ago. So what they seem to be doing is just mass sending the emails out to all who have purchased from one of those, not sure which.