From what I understand, the flurry of blows restrictions apply only to the flurry of blows itself, i.e. to the primary attack routine. The penalty to hit (if the monk is below 9th level and suffers one) applies to all attacks made that round, including additional off-hand or natural attacks and any attacks of opportunity made between the monk's full attack action and his next turn, but it is only those primary flurry of blows attacks (as few as 2 or at most 5) that must be made with unarmed strikes or special monk weapons.
An example would be a 16th level centaur monk (BAB +16: +12 from monk levels and +4 from monstrous humanoid hit dice) who has the feats Martial Weapon Proficiency (longsword), Two-Weapon Fighting, Oversized-Two Weapon Fighting, Improved Two-Weapon Fighting, Greater Two-Weapon Fighting, and Multiattack.
Imagine the centaur carrying a longsword in one hand and a nunchaku in the other. This character could full attack with the longsword as primary, the nunchaku (or an unarmed strike) as off-hand, and secondary natural hoof attacks at +14/+9/+4/-1, +14/+9/+4, and +12/+12. Or he could use a nunchaku/unarmed flurry of blows as primary, the longsword as off-hand, and hoof attacks: +14/+14/+14/+9/+4/-1, +14/+9/+4, and +12/+12.
[/i]^This bit from the FAQ is merely there to point out that if the nunchaku (rather than the longsword) in the above example were used as the off-hand attack, then it couldn't be used with the flurry too, because that would be just like making both the primary and off-hand attacks with the longsword. The off-hand attack is different (and separate) from the primary flurry routine. Because of this, an off-hand weapon used after a flurry clearly need not be a special monk weapon, so why not allow natural attacks after a flurry either?