Nothing is stopping someone from paying the rights owner of a BSD-licensed work for the right to use it without preserving the copyright notice. The analysis is the same as for a GPL-licensed work.
If the argument is that it's better to have BSD-licensed works without paid exceptions than GPL-licensed works with paid exceptions, well... first off, nothing stops the paid exceptions from being "You can use this under the BSD license". Second, this seems like a strategic thing; if most users comply with the GPL, and you raise some money, that seems like a net win compared to everyone complying with the BSD and not providing source despite not paying.
> Assume further that they do not use "interfaces" designed by the GPL source code author.
I'm having a lot of trouble imagining a patch that works this way. If you're patching the program, aren't you interfacing with the program somehow?
I can think of two possible ways. One is that you're actually patching other interfaces (e.g., providing an LD_PRELOAD) provided by more-liberally-licensed software. I don't think that an LD_PRELOAD of POSIX interfaces intended for use with specific GPL software is a derivative work, but I also don't super look forward to convincing my lawyer of what's going on, let alone a judge.
The second is that you're running the program in such a way that you're really wrapping standard I/O and not touching the program itself, but I wouldn't call that a patch. JuiceSSH for Android does this with mosh, for instance; it uses an upstream mosh-client binary (and provides source) in a subprocess of its proprietary UI. On a system like iOS where you can't fork, I could imagine some scheme for running the process in the same address space with some serious emulation. I very much wouldn't look forward to litigating this; it sounds sorta like the VMware lawsuit, which is a huge mess.
If you're providing a plugin through a defined plugin interface, and the software author has said "Use of this plugin interface doesn't subject you to my program's license" (or the plugin interface is an external standard like VST), then you're in the clear. It's worth noting that Linux has an explicit statement that the syscall interface does not subject userspace programs to the GPL. I don't know if such a statement is necessary, but it's nice that it's there. But these sorts of things are definitely not what I think anyone would call a "patch".