Buzzing doorbell due to rectifying diode. (Not an LED)
You are refering to a bicolor LED which has two Light Emitting diodes of opposite polarity.
An LED is a special kind of Diode.
However, all electronic door bells come with a rectifying diode that does not light up.
The discussion thread was not about the light in the button of the doorbell.
The transformers used to lower the voltage going to the door bell are cheaply made, and vary in voltage output. If buzzing occurs when the diode is attached, it usually is caused by the incorrect voltage from the transformer. Ususally located up in the attic, or garage of the house.