I think there is some confusion regarding miles received when trips are company paid as compared with personally paid travel.
No confusion; miles earned as incidental to paid-for travel are not taxable, or deductible, regardless of who foots the bill for the airfare. It's very simple, really. In my personal opinion, this is due less to political pressure than to the very real next-to-impossibility of assigning consistent values to airmiles. When the IRS figures out how to solve that problem, I expect they'll come up with a way to tax them. Taking your example below, who says the miles from Apple are worth $229? Maybe someone thinks they're worth $75. Maybe someone else thinks they're worth $1350.
File how you want to file. I'm quite sure you'd get away with it, because it's really easy to get away with things on taxes.
This. You'll be wrong, because the law is what it is - but do what you gotta do.