Two things;
1) We never see evidence in Chrono Trigger that the Entity was guiding Crono & Co. The best we have is the statement in Fiona's Forrest that the Entity might want people to observe its past, as it is remembering things before it dies. In short, the best we have is that the Entity made Crono & Co observers. By all evidence, Crono & Co made themselves participators.
2) No, TTI does not state that they transcend the laws of space-time, it merely states that they are moving in higher dimensions and are subject to the laws that govern those dimensions.
First, allow me to attempt to explain it in a very every-day sort of way. Imagine you are sitting reading a book (let us say it is The Lion, The Witch, and the Wardrobe). Over the span of about 4 hours you could finish the book. However, for the characters, much more than 4 hours passed; years flipped by for them in what to you appeared to be mere seconds. Susan from the last chapter has no way of traveling back in time to the events of chapter 3, but for you, you can easily flip to that section. Indeed, you can effectively travel through time, from the book's dimensional perspective, precisely because you exist in a higher dimension. If a character were to time travel, they'd have to leave the book's dimension and come into yours.
But even you, the reader, are still limited in your own dimension's sense of time. Perhaps you cross out the 5th paragraph in chapter 6 and write your own. You can never go back in time and undo the marks you made, even though you can easily travel through the book's dimensional perspective of time. You would need to leave your dimension and go to a higher one to have that ability.
Thus, to be short and dirty, "time" refers to time as the average joe in the Chronoverse might experience it, but "time error" (and in turn, TTI) refers to time as we the players experience it. Marle traveled to 600AD not just in the game's time, but also in ours. The only way to undo it would be to travel to before the event in both the game and our world. As a Time Traveler in the game never travels backwards through our time, it would be impossible for them.
And now to attempt a little more abstract of an approach: the laws that govern depth don't apply to 2-D objects, do they? And laws that govern length and width don't apply to 1-D objects?
And while a 3 dimensional object might not transcend the laws of 3 dimension space, a 3 dimensional object certainly does transcend the laws of 2 dimensional space. Likewise, a 4th dimensional object transcends 3rd dimensional space, and a 5th dimension object transcends 4th dimensional space.
However, the inverse is also true. A 2-dimensional object cannot effect 3-dimensional space, nor a 3rd dimensional object 4th dimensional space, nor a 4th dimensional object 5th dimensional space. This is for a very simple reason; a square can't even perceive the depth of a cube, so how could it interact with that depth? A 3rd dimensional object can't even perceive the 4th dimension, so how could it effect it? And the 4th dimensional object couldn't perceive the 5th, so how could it effect that?
Higher dimensions can effect lower dimensions, but not the other way around. Marle traveling back to 600 AD was a 5th dimensional event that changed the 4th dimension. In order to undo that 5th dimensional event, one would need to travel in a dimension yet higher; a 6th dimension. And so on, and so forth.
When an individual travels in time, they must step outside of the normal flow of time to do so. Thus, they go from "Time" (4th dimension) to "Time Error" (5th dimension). If you want to undo something in Time Error past, you would have to step outside of the normal flow of that time. Thus, you would go from "Time Error" (5th dimension) to "Extra-Time Error" (6th dimension). And of course, if you wanted to undo that, you'd have to step outside that flow of time again and into Extra-Extra-Time Error (7th dimension). Theoretically, there needn't be an end to the number of dimensions (proposed limitations on dimensions, as per String, Super String, and M-Theory, are results of calculations on the energy in the universe; thus they limit dimensions because stuff to fill those dimensions are limited).
