The melting pressure and pressure in the liquid at a constant density of ultrapure He-4 (0.3 ppb of He-3 impurities) have been measured with an accuracy of about 0.5 mu bar in the temperature range from 10 to 320 mK. The measurements show that the anomaly on the melting curve below 80 mK, which was recently observed [I. A. Todoshchenko et al., Phys. Rev. Lett. 97, 165302 (2006)], is entirely due to an anomaly in the elastic modulus of Be-Cu from which our pressure gauge is made. Thus, the melting pressure of He-4 follows the T-4 law due to phonons in the whole temperature range from 10 to 320 mK without any attribute of a supersolid transition.