Pretty sure that's because podman-compose literally calls docker-compose under the hood.

e: from the manpage:

"podman compose is a thin wrapper around an external compose provider such as docker-compose or podman-compose. This means that podman compose is executing another tool that implements the compose functionality but sets up the environment in a way to let the compose provider communicate transparently with the local Podman socket. The specified options as well as the command and argument are passed directly to the compose provider."

it calls podman-compose or docker-compose depending on what is installed...

this is literally what manpage you quoted says too

That's the "podman compose" wrapper command. podman-compose (the implementation referenced in the first sentence of your quote) does not call docker-compose: https://github.com/containers/podman-compose