My highschool history teachers insists that after the collapse of the Soviet Union in 1991 and the opening of the archives, there was evidence and post-revisionist theories to suggest that Stalin very much knew of the operations conducted by the NKVD and personally signed death sentences, even of people taken under protective custody.
This greatly contrasts with my view that the NKVD's authority was not kept in check and they often conducted executions without the central authorities knowing, and that Stalin gave Beriya too much freedom, which meant the secret police could remove 'opportunists' and 'careerists' as they pleased. Does anyone have anything to support either claim?
In short: yes but with a nuance. The central authorities (ie Stalin and the Politburo) were fully aware of the scale and nature of the repression in the 1930s. For all its mass character, the impetus and direction for the violence came from the top down. This was managed via:
Decree. We don't know exactly why Stalin decided to launch the 'mass operations' (ie broadening the purges beyond the party in a process that ultimately killed hundreds of thousands) but in July 1937 he approved NKVD Order 00447 which did exactly that. The language of this order draws wholesale from previous telegrams from Stalin on the repression of kulaks. In was in the same period that Stalin explicitly ordered Ezhov to begin the 'national operations' against ethnic Germans.
Quotas. The mass operations were managed via a quota system in which each region had a set number of 'enemies' that it was expected to kill. The actual quota setting happened at a regional level (ie the Moscow party organisation would propose to execute X number of 'hostile' elements) but these were signed off and managed at the centre. Stalin personally was involved in approving/amending these regional quotas, even if this sometimes meant reducing the numbers.
Albums. At times Stalin literally signed off on those who were to be executed. In the case of party/state elites this took the form of a list that was submitted to him. Elsewhere, when the quota system wasn't applied (ie to certain 'national operations'), central control was maintained via the 'album procedure'. This required the regional NKVD bodies to draw up a short summary of operations, along with a list of suspects, which were sent to Moscow for review. Only when the latter gave the word could executions begin.
So there was relatively strong central control over the scale of the violence. Even when this was weakened in Sept 1938, with the establishment of special troikas, there was conditions in place to govern the latter's behaviour. This is why the violence could be curtailed fairly easily (and Ezhov removed) in Nov 1938. Any suggestion from Stalin that he was not in control or aware of proceedings should be seen (much like his infamous Dizzy with Success response to collectivisation) as him covering his ass.
The nuance lies in those who were targeted and the degree to which Stalin genuinely thought that those executed were spies, wreckers, etc. The latter isn't something that can be easily answered - even in private correspondence Stalin used the same robotic slurs that he did in public. He did accept that there were some excesses and certainly at some local levels the violence was chaotic rather than controlled. (in The Road to Terror Getty paints the Soviet state as an almost feral creature lashing out blindly in all directions). But that's not particularly relevant when it comes to the question of 'innocence': he still played a key role in a programme of mass extra-judicial executions.
Paul Hagenloh goes into a fair amount of detail on the mass operations in Stalin's Police. Helpfully, as the title suggests, he fixes this in the context of policing throughout the Stalinst period.