I originally interpreted this to include message on forthcoming virtual gifts, which do get displayed publicly on the profile. But I stand by my thought even when it's privately sent gifts. It is harder (not impossible, but harder) to send a harassing message in points/paid time/rename tokens by themselves; a lot of disallowing of anonymous contact is intended to deter or inconvenience harassment. With the ability to turn off notes on anonymously sent gifts, someone could allow friends to send points etc. anonymously and accept the chance that a harasser could also be sending some, but block that avenue of contact as far as anonymous harassment is concerned.
no subject