>> What I would do is help myself to their patch, if it's worthwhile and backport it to the BSD-licensed version.
>> The code is my copyright, and the patch is a derived work of something of mine; therefore I own it and it falls under my license.
That is completely incorrect. You have no rights to the patch just because it is a derivative work. You have the right to prevent distribution of derivative works (not to own or distribute), but you gave that up with the BSD license which expressly allows it.
You're also wrong about the license of the patch. The author of the patch gets to chose it. For GPL licensed software the condition of redistribution is that all derived works be distributed under the GPL as well. If you don't GPL it, you lose your permission to redistribute the original code and derived works.
BSD and MIT licenses don't include this restriction, so you're shit out of luck with making any claim on that patch.
>> The code is my copyright, and the patch is a derived work of something of mine; therefore I own it and it falls under my license.
That is completely incorrect. You have no rights to the patch just because it is a derivative work. You have the right to prevent distribution of derivative works (not to own or distribute), but you gave that up with the BSD license which expressly allows it.
You're also wrong about the license of the patch. The author of the patch gets to chose it. For GPL licensed software the condition of redistribution is that all derived works be distributed under the GPL as well. If you don't GPL it, you lose your permission to redistribute the original code and derived works.
BSD and MIT licenses don't include this restriction, so you're shit out of luck with making any claim on that patch.