What are the risks associated with getting your eyebrow pierced?

Technically things listed on the scare tactic list are probabilities, although some are a very low risk and some may be much higher. Your greatest risks with any piercing are infections, starting with bacterial (from improper sterile technique or an exposure soon afterwards), scarring or after effect from your body rejecting the piercing, then more serious infections (blood borne stuff, usually from improper piercing techniques again), then you actually get to the rarest of chances that an infection would be so bad as to enter the body or brain.

Usually something un-aesthetic happens, most often from a rejection where the body just won't heal the piercing, or the piercer lines the jewellery up badly somehow. Your greatest danger is from an improperly trained piercer, someone who is not trained in preventing disease transmission or using proper sterile piercing techniques. Boiling something is NOT the same as running it through an autoclave (the medical cooker that you really need to sterilise equipment).