You are correct insofar that the visualization model of a bowling ball on a trampoline is misguided and misrepresentative of nature. However, the Universe Is Flat claim is not addressing spacetime "curvature" and its relation to gravity. Think of a complex 3-D configuration of eletrical charges. If you zoom way out, you can treat the cumulative electrical field as if it's a one-dimensional, singe point of charge. Similarly, if you zoom way out from the observable universe, it's overall shape inside the unobservable universe tends towards being co-planar. Observable "stuff" tends to clump along a plane and the metric expansion of the universe tends to also move along this plane. There is nothing to stop energy/matter or metric expansion from moving or existing further along a Z-axis, but from all observations, it just tends not to (on a cosmic scale).