Bagso
I don't see a contradiction. It's entirely reasonable for BA to resist an increase in HAL's charges to fund R3. Any sensible business would do that. Remember, however, that BA strongly resisted the increase in charges to fund T5. They lost, but did that affect their growth at LHR? No, they continued to hoover up slots, eg by acquiring BMI.
If R3 goes ahead I would hope that the increase in HAL's charges might be lower than implied by Davies. But even if an increase of (around) £10 is required, I really don't think that BA would suddenly throw in the towel. All the evidence (such as slot values) points to Heathrow's charges being well below market clearing levels. BA might shout and scream, as they did with T5, but they'd pay up in the end.