Does isotropy imply homogeneity?

When MTW say the universe is isotropic, they mean it is isotropic everywhere i.e. at all points in the universe.

It's easy to construct universes that are isotropic at a single point and not homogeneous, for example CuriousOne's suggestion of a ball with density that is a function of distance from the centre. However this ball is only isotropic if you are at the centre of the ball. If you require the ball to be isotropic everywhere you necessarily require it to be homogeneous.

MTW actually give you the answer (in a technical form) to exercise 27.1 in the paragraph just above the exercise next to the side note:

Isotropy implies fluid world lines orthogonal to homogeneous hypersurfaces