Absolutely. And any coyote brought in by someone else would promptly become "property" of my non-profit, and any bill on it would be mine unless the finder made a donation. It's illegal to keep wild caught native animals here, so I would not be giving it back even if someone brought it in. I'd patch it up and turn it loose as close as possible to where it came from.

ALL the wildlife I work on is "free"... All bills are paid by donation, most of the donations are made by me. The state pays me back for none of it.