What testimony are you referring to? And out of curiosity, have you had a chance to read Rappaport's book?
Last Act of A Tragedy:
The military commander of Ekaterinburg, Goloshchyokin went to Sverdlov in Moscow, and was specifically denied permission to execute the IF. Lenin told Sverdlov that he specifically wanted the IF brought to Moscow for a public "show trial"
Sverdlov's exact words;"Filip, (Goloshchyokin) tell the comrades that the ARCEC does not give official sanction to an execution." This telegram is reproduced in the book as one of the plates.
G.'s testimony, also in Last Act:
Goloshchyokin went to see Sverdlov in Moscow about allowing the Ural Soviet to execute the IF in early July 1918. Sverdlov consulted Lenin about what to do with the IF. Lenin spoke of bringing the tsar's family to Moscow for an open trial of Nicholas and Alexandra. "It must be an All-Russian trial only! With publications in the press. It is necessary to count what human and material losses to the country were caused by the autocrat during his reign. How many revolutionaries were hung? How many people died in penal servitude and in a war nobody needed? He must answer for that, facing all the people!...It is the incomprehensible Russian credulity [of the Russian peasants] that must be discredited at the open trial of Nicholas the Bloody..." as reported being said by Lenin by Goloshchyokin.
Further, the exact resolutions, also from Last Act:
Extract from Protocol No. 1 of the ARCEC Presdium meeting about the shooting of Nicholas II
July 18, 1918:
HEARD: The report about the shooting of Nicholas Romanov (telegram from Ekaterinburg)
RESOLVED:After discussion, the following resolution was accepted: The ARCEC in the name of the Presidium, recognizes the Urals Regional Soviet's decision to be correct. To instruct Comrades Sverdlov, Sosnovsky and Avanesov to compose the appropriate announcement for the press...
From Protocol no. 159 of the Council of People's Commissars meeting about the shooting of the royal family:
July 18, 1918
Chairman V.I. Lenin. (Trotsky is present among others.)
HEARD: 3. Special announcement by the ARCEC Chairman Comrade Sverdlov about the shooting of the former Tsar Nicholas II according to the sentence of Yekaterinburg soviet and about the ratification of this sentence by the ARCEC Presidium...
RESOLVED: Accept for general information.