This statement on Wikipedia is merely intending to separate the agency of determining "What is pain?" from the nociceptors. Nociceptors can be activated by a number of stimuli that reflect possible damage (i.e., a possible threat): this could include signals released by cells that are actually damaged, it could include hot temperature, it could include certain types of pressure or touch.
The decision about whether a particular stimulus is sufficiently threatening to warrant a response (which could include things like reflexes all the way up to the perceptual and emotional experience that we refer to as pain) is made in the spinal cord and brain. At the level of the nociceptor, "possible threat" and "real threat" aren't any different: the nociceptor is just reporting the possibility of the threat. The CNS makes a 'decision' about how to respond.
This system is really no different than the other sensory systems, they all carry some information to the CNS which then interprets that information.