If you use mostly closed-source software, that should not affect you negatively - on the contrary, the vendor should then be held to even higher standards to treaty you well than if you were using open source, since the vendor has effectively removed from you the opportunity to do your own quality checks.

I haven't thought about the re-branding issue, to be honest. I also don't think it's raised in the consultation, and no way to address (or assess the need to address) the problem springs immediately to mind.