Context. Abreu et al. (2012, A&A. 548, A88) have recently compared the periodicities in a 14C - 10Be proxy record of solar variability during the Holocene and found a strong similarity with the periodicities predicted on the basis of a model of the time-dependent torque exerted by the planets on the sun's tachocline. If verified, this effect would represent a dramatic advance not only in the basic understanding of the Sun's variable activity, but also in the potential influence of this variability on the Earth's climate. Cameron and Schussler (2013, A&A. 557, A83) have seriously criticized the statistical treatment used by Abreu et al. to test the significance of the coincidences between the periodicities of their model with the Holocene proxy record. Aims: If the Abreu et al. hypothesis is correct, it should be possible to find the same periodicities in the records of cosmogenic nuclides at earlier times. Methods: We present here a high-resolution record of 10Be in the EPICA Dome C (EDC) ice core from Antarctica during the Marine Interglacial Stage 9.3 (MIS 9.3), 325-336 kyr ago, and investigate its spectral properties. Results: We find very limited similarity with the periodicities seen in the proxy record of solar variability during the Holocene, or with that of the model of Abreu et al. Conclusions: We find no support for the hypothesis of a planetary influence on solar activity, and raise the question of whether the centennial periodicities of solar activity observed during the Holocene are representative of solar activity variability in general.