I as well have heard similar things my entire life, and I generally won't use BP either. I believe many moons ago, there might have been a legitimate problem.
Today, I'm highly doubtful, but it shows how long things like that can damage a company.
Driving around on summer tires in winter is borderline retarded honestly.
Why take your life, and possibly others into your hands becuase you didn't feel like switching tires. You could probably cut a brake hose and "make it" to work using the ebrake, but you'd realise that being able to stop reliably is imporant.