Yes, if you ask about a tag on a commit that you don’t have git won’t know about it. You would need to download that history. You also can’t in general say “commit A doesn’t contain commit B” as you don’t know all of the parents.
You are completely right that –depth=1 will omit some data. That is sort of the point but it does have some downsides. Filters also omit some data but often the data will be fetched on demand which can be useful. (But will also cause other issues like blame taking ridiculous amounts of time.)
Neither option is wrong, they just have different tradeoffs.