Why do some Centrino chipsets and PCI-Express cards say Not for Lenovo/HP?

With Lenovo, the problem is that the BIOS has a whitelist of permitted PCI-Express cards and will refuse to boot with any unauthorized PCI card (source), i.e., they want you to buy only their own PCI cards. There are often ways around this, including hacking the BIOS, hacking the PCI-Express card (replacing the ID information). If you boot a non-whitelisted card your bios will throw the 1802 error,

1802: Unauthorized network card is plugged in - Power off and remove the miniPCI network card.

I suspect the same is true for HP.

Lenovo uses a WiFi antenna design that could exceed the maximum radiated power permitted under FCC regulations if used with a card that emitted the maximum power permitted. To avoid a configuration that violates FCC regulations, Lenovo designed the BIOS only to permit WiFi cards that were tested with its antennas to be used.