This is the situation:
Client = a company that needed an application built.
Headhunter = technical requiter that has the contract with the client for the application.
Me = a sub contractor to the headhunter. I worked as a 1099 subcontractor to the headhunter when I built the software for the client.

Here's my question:
The headhunter asserts that it owns all of the code I used in building the application for the client, even the foundation class libraries that I've used on different projects for other clients.

My understanding of copywrite law is that they don't own it, even though there is a clause in the contract between me and the headhunter that they use to say it does. Who's right?

TIA