I think anyone can list a Github profile as part of their resume, absolutely. That's why I said you should ask questions about the contents of that Github profile. Explain why you built X and how Y works and if you could do Z differently, what would change? What were the biggest problems with this project and what did you think would be hard about that project but turned out to be easy? And so on.
IMHO, there's no need for whiteboard coding.
Having said that, if you are going to ask me to do some whiteboard coding, I would greatly prefer something like you described -- a high level response that tests my thought processes. You can see my code on Github, I shouldn't have to write some on a board. But I'll be happy to explain thought processes while solving a problem.
I can see both POVs, and they definitely have merit. In my own interview for my current job, I was very happy to not have to code anything - the team leads who interviewed me already found it obvious that I was extremely smart & knowledgeable despite having less than a year of experience.
Not that I would have minded coding on the fly or answering stupid brainteasers - I grew up figuring those things out. Those leave me with negative impressions of the company though, and may lead me to demand a higher salary to accept a position.
IMHO, there's no need for whiteboard coding.
Having said that, if you are going to ask me to do some whiteboard coding, I would greatly prefer something like you described -- a high level response that tests my thought processes. You can see my code on Github, I shouldn't have to write some on a board. But I'll be happy to explain thought processes while solving a problem.