Exactly. Always compensate for the variation in boiling point for your elevation.
Also, NIST has an interesting publication concerning the recalibration of mercury in glass thermometers, and among the interesting information it contains, is a section about how to prepare a proper ice slush bath for calibration at 0 degrees C.
The main takeaway from that is that you want to shave the ice into particles, as they say, "the consistency of a snowcone". That reference made me laugh the first time I read it. The world's premier authority on metrology actually found "the consistency of a snowcone" to be the best way to describe this highly technical parameter!
Also, they want you to use deionized or distilled water for both the ice and the water. And you should continually siphon off the water so that the water level is just below the top of the ice slush.
The idea is this:
When you freeze ice in your freezer, the freezer is well below freezing. And your ice cubes are, therefore, well below freezing temp. If your thermometer probe is in contact with an ice cube, it will likely be exposed to a temperature below freezing.
But if you've shaved the ice cubes into particles "the consistency of a snowcone", and have just enough water in the slush mix, these small particles will come to equilibrium with the temperature of the surrounding water very quickly.
So the whole works will be at the exact freeze-melt point for water, and not only that, the heat capacity and thermal conductivity of the slush is fantastic. A probe or thermometer inserted into such a slush will quickly and accurately come to 0 degrees C.
Properly prepared, such an ice slush is fantastically accurate.
I am not kidding that I actually bought several snow cone machines for the labs where I used to do thermometer calibrations. I also had a few small thermos units and even small styrofoam shipping boxes that I used to contain the ice slushes.
I never used boiling water baths, but instead used what amounts to the laboratory version of a Sous Vide heater-stirrer gadget along with a NIST-traceable reference thermometer for warmer temperatures, and a "dry block calibrator" that I built for higher temperatures.
But using distilled or deionized water, brought to a boil, and knowing your elevation and the boiling point at that elevation, is very good.
You want to use distilled or deionized water for both the ice bath and the boiling point calibrations because impurities in the water can decrease the melting point and increase the boiling point.