The other reading gives God a much more central role in the system. God is not the fill-in perceiver in this view, rather it is God's perceptions of things in virtue of which they are originally said to exist. All ideas (and spirits too, Berkeley seems to suggest) exist in God's mind, and we only gain access to these when He chooses to reveal them to us. It is only God, then, that is external to finite minds. There is no world outside of God.
Given this reading of Berkeley it is easy enough to see why he thought that his idealism was a powerful antidote to atheism. Anyone who accepted this view of the world would need to accept God as a central part of it. God cannot easily be removed from this system, as he could be from Locke's or Descartes' systems; remove God from the system and there is no system. The system boils down almost exclusively to this: objects are ideas in the mind of God; objects exist because God perceives them. How could we replace God in such a system? What could be responsible for keeping all our ideas in existence and causing our sensations, if not God? It is for this reason that all later idealist systems were also highly spiritualized, even if not religious in a traditional sense. Since material objects cannot play this role, and we ourselves certainly cannot play this role, that leaves only some spiritual being, greater and more powerful than ourselves. In this, at least, Berkeley was absolutely right: one cannot be an idealist and an atheist at the same time; to believe in idealism, is to believe in a spiritual being who grounds the entire world.
There is also another related position that has been frequently attributed to Berkeley: phenomenalism. According to this interpretation of Berkeley's thought, the answer to the question, "how do things stay in existence when I close my eyes?" has nothing to do with God. Instead, goes this line of reasoning, things stay in existence because their existence is not to be actually perceived, but only to be possibly perceived. A thing, on this phenomenalist understanding, is a permanent possibility of sensations. To say, for instance, that there is a table in the other room, is just to say that if someone were to go into the other room, they would have sensations of a table. Both Mill and Russell actually ascribed to a view like this one, which rejects the claim that esse is percipi and says instead that being is to be perceivable. There is some textual evidence that suggests that Berkeley ascribed to this view as well. For instance, at the end of the third dialogue, Philonous says that when the Bible speaks about God creating the world, what it means is that God set things up so that if there were perceivers around they would have had such and such sensations.
There are many difficulties that arise from this view. In order to fulfill the antecedent of the conditional (the "if " part), you need some mind- independent understanding of what the conditions are. For instance, in order to make the above claim about the table, you would have to believe that there really is a room you could walk into. Perhaps, though, we could understand the antecedent as follows: If I were having standing in the other room sensations then I would have table sensations. But still another worry remains: what grounds these conditions? What makes it the case that if I had standing in the other room sensations I would have table sensations? We want to say, of course, that what grounds these conditions are some facts about the world: the fact, for instance, that there is a table in the other room. But Berkeley, as an idealist, certainly cannot say this.
Berkeley probably does ascribe to something like this phenomenalist understanding of existence, in addition to his plain idealist understanding, but his phenomenalism can only be understood if we add in the central role that God must play in his system. It is God, on his view, who grounds all conditionals: it is because of God that if I had standing in the other room sensations, I would have seeing table sensations. These ideas maintain this relation to one another because God chose to place these ideas in this relation to one another; they go together constantly in His perception, and so also go together constantly in our perception.