The cost of these systems is 100% in the electronics. What I presume is going on here, is that Amazon (like SpaceX) has developed custom RFICs, which handle both uplink and downlink in a single package, thus requiring the apertures to be overlapping. The advancement is in having developed a better IC, the size reduction is an indirect outcome.
If Kuiper is taking a very different approach, more akin to Kymeta or ThinKom, the original statement might be credible, but the aperture looks too thin for that to be the case.