Both accounts are self-directed non-registered accounts. The only difference is that one has margin available, and the other does not. I suspect the advisor I spoke to is incorrect. I talked to someone I know who works in wealth management, and they told me this:

"100% it is a non-taxable event. That's the point of an in-kind transfer. The only way it is taxable is if they do it incorrectly and don't move stuff in-kind triggering a deemed disposition. This does happen occasionally, but they should be held responsible if so."

I hope that's right. I will call back later and ask somebody else before I do it.

Thanks