You're absolutely spot on there. The reason they're being picky, is if you export only solar, that generates them a REGO cert. They can sell that on to the likes of Octopus who can then claim all power is 100% green.
If you're exporting from battery, you may have charged it from the grid, so no REGO, and no money made that way.
So nothing to do with technical limitations, purely financial.
Don't worry, I expect to be told that's wrong, that we can't generate REGO's, but you get the gist of my thinking.