cp and scp

I am in a directory with a number of folders, each of which has a file named out.csv

I would like to copy only these files, while preserving directory structure.

If I do scp -r gusl@ubc.ca:my-project/*/out.csv my-project/ then all the copies of out.csv get copied into the base of my-project, erasing each other.

I want to specify which files match separately from the root directory from which I am recursively copying.

Is this one of the rare uses of the --copy-contents option?