I had thought it was necessary to turn off “use wikilinks” to make Markdown likes behave like wiki ones, but apparently not.
I understand expecting Obsidian to preserve the existing format, but updating a link sounds exactly like such a circumstance to me (and is consistent with how it has treated my wikilinks). Obsidian is replacing the old link with a new one.
“Shortest path when possible” essentially produces wiki-like behavior. It allows you to link to any file in the vault folder by using only its name (unless another file has the same name; then a path must be used to reach the right one). Doing this with Markdown syntax is unusual of Obsidian, but I guess it doesn’t violate any rules, since Markdown doesn’t restrict (or barely restricts) what link destinations can look like.
If you don’t want the behavior that setting is meant to produce, don’t use that setting. Unfortunately (since it looks like you’re managing a website) the other options have their own issues. Obsidian’s handling of relative links is buggy, and the “Absolute path in vault” setting produces links without the leading slash required by other apps to recognize them as root relative. (Related feature request: Start absolute path (path from vault folder) with a leading slash / .) People (including Obsidian’s CEO) use Obsidian to manage websites anyway, so presumably this can be worked around, but I don’t know the details (someone in the FR thread mentions adding the leading slash manually 
).