No, not correct.
Your laptop's music should not be touched when you sync with an iPhone, and you do not need to subscribe to itunes match to sync directly over USB or Wi-Fi.
When syncing anything on the iPhone that is not part of the iTunes Library on the computer will be deleted from the iPhone, but the library on the computer remains untouched. The library on the computer is the master basically.
iTunes Match is used to match or upload your music library from a computer to the cloud, so it can be accessed by other devices such as your iPhone without needing to sync directly to the computer.
I believe its iTunes Match that can let you reclaim media onto a computer, since its the one that provides non DRM protected files for the matched and uploaded music, while all tracks in Apple Music are protected, so while they can be downloaded, they cannot be accessed if the subscription to it is discontinued.