You can do that as well (at least some of the time). Just use the automated settler command (k), and if the computer thinks you need irrigation somewhere, it will do it without access to water.
The reason the AI can irrigate without access to water is probably because it would have been too difficult to program it to do so. Having to irrigate from a water source alters order of irrigation and the value of city sites, but only some of the time.
I wouldn't call much (if anything) of what the AI does "cheating." The point of the AI civs is to create an environment that makes growing your own civ more enjoyable and interesting; if it has to follow somewhat different rules than I do, so be it.
In any case, the human gets one major "cheat" in the game: it gets a last chance to build a wonder, and beat the AI to it.