As the public impeachment hearings concluded Thursday, National Security Council official Fiona Hill’s testimony echoed and reinforced the concerns that have been raised by other members of the foreign service who have testified about how the president diverted from official administrative channels in dealing with foreign leaders. But that testimony from current and former members of the administration risks pulling Democrats away from what should be the focus of their inquiry, namely the president’s unprecedented withholding of foreign military aid to try and compel a foreign power to investigate a domestic political foe.

The hearings instead often seemed to focus on Donald Trump’s shadow diplomacy, as witnesses stressed their concerns about how the “official foreign policy” of the U.S. could have been undercut through the use of “irregular” and unofficial channels that cut out the foreign service staff and contradicted official policy. Even coverage of the impeachment hearings in legal circles often seems to frame the impeachable act as the president’s attempts to communicate with the foreign leaders “outside of the regular channels of the government,” and in contravention of “normal policy process.”

Thursday’s concluding testimonies highlighted the Democrat’s members’ eagerness to pursue this line of attack, as their counsel, Daniel Goldman, poked and prodded witnesses: Which members of the diplomatic staff were excluded from one-on-one meetings with the Ukrainian president and his aides, and why? Did the president routinely disregard the advice of his senior officials in favor of following Rudy Giuliani’s advice? What internal protocols were ignored in scheduling and carrying out discussions with Ukrainians?