I generally buy budget tyres - and change then at 3mm tread which is safer than trying to squeeze every mile out of your premium tyres.
I had a Audi up my chuff on a fast A-Road at about 80mph driving my missis's Citroën on budget Chinese all-season tyres, I was overtaking (not lane hogging) then I spotted huge puddle ahead, I just took my feet off the pedals in anticipation of the incident, I hit the standing water - no drama, The Audi pirouetted off into the Armco.
Budget tyres today are better than premium tyres of ten years ago, if you're using the last 20% of grip in normal circumstances you either cannot anticipate the road properly or you need to find a race track. The Nexens I put on my Jag XJ8 had more grip wet and dry than the o/e Pirellis and they cost half as much. There's a lot of scaremongering about budget tyres because the big companies make a fortune selling you over-priced "premium" rubber. Yes the premium tyres are probably slightly better - but that's about it.