I agree it doesn't seem right to me either, which is why I posed the question. Although, under my most recent scenario, the UK Company will be making payment to my US account and I will be a self employed contractor in the US and submit invoices to the UK company from the US. I will indeed be travelling to the UK a minimum of 1 week a month but I don't believe US citizens are bared from doing that as a visitor. I will not be establishing residency in the UK, where that could be viewed as falsifying circumstances.

Thanks all for the input.