The Short Version
The claim is scientifically accurate. At water's triple point (~0.01°C and ~611 Pa), solid, liquid, and gas phases coexist in equilibrium, meaning the conditions for both boiling and freezing are simultaneously met. This is confirmed by NIST, peer-reviewed research, and multiple academic sources. The minor caveat: "simultaneously boil and freeze" slightly overstates the drama — it's thermodynamic equilibrium coexistence, not necessarily vigorous concurrent boiling and freezing — and the required pressure is just 0.6% of normal atmospheric pressure.