News from AmEx Customer Service: NO points or miles from AmEx as they regard TCC purchases as cash transactions

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So there you have it: two entirely opposing answers from AmEx just a few days apart

. This time, it does look authoritative as they took 2 1/2 hours or so to respond.
So now purchasing a £3,000 TTC + £20 fee with a Tesco c.c. could earn 1510 points = 4,832 BA miles. Using a fee-free bmi c.c. could earn 4,530 BD miles. Both subject to verification from
RJB and
TheMajor, of course, and ignoring fees for cash withdrawals. Do my figures work out?