Good heavens no. This has not been the case for a decade or more!

The first version with snap as standard was 16.04 in 2016:

https://ubuntu.com/blog/canonical-unveils-6th-lts-release-of...

However Ubuntu Core, its immutable distro built entirely from snap packages, was launched in 2014 and there was a Core version of Ubuntu 12:

https://old-releases.ubuntu.com/releases/ubuntu-core/release...

There are about half a dozen cross-distro packaging schemes for Linux, including Nix, Guix, AppImage, Flatpak, Snap, and 0install.

However two are mainstream and supported by large vendors: Flatpak is from the GNOME organisation and is backed by Red Hat and Fedora, and Snap is a Canonical project and part of Ubuntu, the single most widely-used distribution by a considerable margin.