Short version: The AI players have access to the same information that human players do, and the game itself treats AI players and human players identically.
There's two aspects to the claim that the AI cheats, the first being that the the game gives the AI advantages, and the second aspect being that the AI knows what the next roll of the die is.
For reference, I am using the post written on the steam forums from jaxon, one of the developers.
The AI does not have special access to any hidden information that a player would not have.
AI players do not know what is on top of the various decks (and they may not even remember what has been drawn from the various decks). they also do not know what the next roll of the die will be (more on that later), and they don't know what spell cards each player has (I suspect the AI doesn't know this even if they're using a character that would allow them to know, though jaxon hasn't specified if this is the case or not).
Outside of the use of runestones and character-specific effects, the game does not offer any players, AI or human, special advantages over another player. Anything an AI could do, a human player could do in the same situation.
All players take their rolls from the same random sequence of rolls, which is determined at the start of the game. The sequence of rolls is generated using the WELL512a RNG algorithm* and is used for every die roll in the game, regardless of who the roll is for. As previously mentioned, AI players do not look ahead in the sequence and as such do not know what the next roll is. I have actually observed (with surprising frequency) AI players reroll a result of 2 on the Grim Reaper (lose a follower or one life) and get a 1 (die on the spot) as a result, which they wouldn't do if they knew what the next number in the sequence was.
As an aside, one of the naive user-made tests for this was to make a save and then reload the save over and over to observe the AI players doing the exact same thing and getting the exact same results. This is due to the fact that the sequence of numbers for rolls is kept in the save file for the game, which renders the test less useful for proving either way that the AI does or does not cheat. This saving behavior is also intended to prevent people from save-scumming games to get different results.
* - The randomness of the WELL512a algorithm itself is beyond the scope of this question, the important part is that the sequence is sufficiently long and random, to the point where most casual observers would have trouble distinguishing it from the actual output of a physical 6-sided die.