Yes, that was one factor for sure. But it was actually really complicated, quite mind boggling in fact. The thing is that, in spite of Stalin being pretty much the only effective external support the Spanish republic had, the communists inside Spain were pretty much a marginal group when the war started, and had to resort to all kinds of intrigues to get support from both the population and the, still, official government, and also to had get rid of rival groups, like the ones you mentioned.
Yeah - I read Homage to Catalonia again recently - I have read The Battle for Spain by Antony Beevor a while back but as you say, it is quite complex - I need to read it again!