Even now that doesn't get you all kind of access, only some. You have to assume magical abilities at persuasion of people to do that.

The USSR couldn't bribe the US into surrendering during the cold war, for example.

If superintelligence is actually achieved, magical (as per Clarke's third law) persuasion abilities aren't that much of a stretch.

Furthermore, a sufficiently advanced AI could bribe someone with things that no human could believably provide. Essentially unlimited knowledge, money, power...

They are a super stretch given how stubborn humans are and the difficulties in swaying them (up to and including dooming themselves).

Your second point is again attributing magic abilities to an AI. It is unclear that it would have godlike powers.

Define godlike...

The ability for a human to input information is insanely slow. Like in the tens of characters per second range. You cannot hold individual conversations with more than a few people at once. 3 people talk at once and you lose the ability to process the incoming audio. You read text one line at a time. You have two eyes that focus on the same thing and only have a very tiny high fidelity visual processing space.

In books like the bible they talk of entities that can listen to and respond to all of humanity. Is that outside of the capabilities our computer systems have now? To listen to, catalog, classify, then respond to everything every person on the planet says?

So I ask again, what is godlike?

The biblical God isn't restricted to just passive and communication powers, is it? Godlike powers include active abilities way beyond human capability. What is often brought up in the context of AGI is the ability to persuade anyone of anything, ability to solve biological or physical problems beyond our ability or comprehension, entering any system undetected - not even sure a precise definition is needed as it usually boils down to what looks like magic to us.