The only requirement in my area is that all thermometers on the bar must be accurate. Our inspector checks them on every visit. SO... the bigger concern for you may be that they are out of whack.
You should recommend that yours be calibrated and offer to do it. Quite simple for most - bring some water to a full rolling boil, immerse the probe, use a wrench (or the caffeine wrench, or pliers, etc) to hold the thermometer by the hex on the back of the "head", and turn the head until the needle is at 212 (or the red triangle on many models). There is some variation in the boiling point with altitude, so check your local boiling temperature if you are somewhere like Denver and set it to that temp instead.
While there is a possibility that this varies state by state, in Oregon this is not true. It's an urban legend. As i said before, the only time that is the case is if you are doing hot holding. It's perfectly legal/safe to serve a drink at 120 degrees if you want to. Consider kids hot chocolate or gibraltars.