It's mathematically simple for a space to loop without being curved locally, although I am under the impression that there are physics reasons to infer we don't exist in such a space.

The pac-man universe acts euclidean until you have universe-sized effects. For example, a circle will satisfy circumference = diameter * pi until its diameter is greater than the span of the universe. Basically the universe could 'hide' the fact that it is a torus from pac-man by simply being really large.