|3. A tire will burst if the "max press" number on the sidewall is exceeded.|
A new quality tire will not burst even if the "max press" is exceeded by a very large amount. All bets are off if the tire has been damaged or it's fitted on a cheap or damaged wheel.
Coupled with the "max load" number, which is found near to "max press" on the sidewall, you can know the maximum load-carrying ability of a tire. Know this: It's air pressure that allows the tire to carry a load. At one pound per square inch (psi) of air pressure a tire can support no weight. To increase its load-carrying capacity, air pressure must be increased. (Imagine a plastic soft-drink bottle: With the top off, it's easily crushed, but new and unopened it can support a grown man.) However, at some pressure, adding more air to the tire will not provide increased weight-carrying capacity: That's what the "max load/max pressure" means.
4. The "max press" on the sidewall is the proper inflation pressure for your tires.
Fewer believe this than the previous item, but the misconception is widespread in the law enforcement community.
The proper inflation pressures for tires are determined by the automaker (in concert with, but not by, the tire maker). The government now requires new cars to have that recommended pressure on a placard located on the driver's doorjamb. On older cars this placard was often on the doorjamb, but depending on the car company, could be on the trunk lid, glovebox door, console lid, or fuel door. If you can't find the recommended pressure placard, look in your owner's manual or call your carmaker's customer service department.
Inflating the tire above the car manufacturer's recommendation may make it more susceptible to damage from potholes and will reduce ride comfort. However, it will likely increase race-track-style at-the-limit performance. (I suspect this is why highway patrolmen run high tire pressures.) Back in the day when I raced showroom-stock cars, the rules required everyday tires rather than the made-for-racing specials now allowed. We always set the pressure far above the vehicle maker's recommendation. When I ran front-wheel drive cars, I often used extremely high pressure in the rear tires: I was trying to reduce rear grip so the car would turn better in the middle of the corner.
5. Budget-brand tires are as good as big-name brands since they're built by the same
As with most products, rarely do you get more than what you pay for.
It's easy to see how this misconception developed. Each tire company has a premium brand upon which it focuses its research, development and testing. In addition, almost all produce other brands. Many build tires for others—such as auto-parts stores—to sell under the store's brand. As you progress down this list, development and testing quickly drop to no more than legal requirements. The R&D from the premium brand often—but not always—trickles down into the budget brands. So maybe the difference is so small, you can't tell difference. Or maybe not.
Our litigious society means that you can be fairly certain that discount and private brand tires built by big-name companies will resist failures as well as that company's premium offerings: If the store-brand tire fails, the tire company that made it gets sued just as if the tire boasted a premium brand name. However, things like tread-life, traction, ability to resist deep water, noise, and comfort will probably—but not always—be inferior.
It's easy to argue that tires are the most complex, most important, least understood, least appreciated, and least maintained component on any vehicle. Serious drivers will tell you they know that already.