Traditori Viridiani

A player is poisoned if that player has one or more poison counters.

The player must be poisoned when Viridian Betrayers deals damage in order for Viridian Betrayers to have infect. If the player has no poison counters, damage dealt to that player by Viridian Betrayers will result in loss of life, even if it's dealt at the same time as damage from another creature with infect.