Even if you look at the terms used : https://snapcraft.io/docs/core/store :
"The main way of distributing snaps to snapd systems is through the Ubuntu Store"
So indeed there is the "other store" section which mention you can host your own store but it's clearly not emphasized.
Even the term of Snap "store" vs Flatpack "repo" seems to indicates a more decentralized/agnostic direction of Flatpack.
On flatpak.org/apps.html you can see LibreOffice hosted by documentfoundation.org and MonoDevelop hosted by mono-project.com. They're not all hosted by their respective foundation/website, but still it kinda seems like it is the direction flatpack is pushing for.
So "technically" they all are distro-agnostic, but in terms of distribution system one is pushing for a centralized Canonical-hosted store while the other seems to be going towards a "each foundation will host their app"