"A brand that has invested in advertising is more likely to care about quality and more likely to fix problems, out of brand protection."
A brand that invests heavily in advertising may assume that that's all it needs to do. In fact it may not be able to invest in quality because all the money's gone on the adverts.
How do your data mining algorithms obtain figures on people who've gone elsewhere because of the ads? Occasionally there may be strong negative feedback - e.g. my complaint to the MD of the car sales firm - but mostly people will go quietly elsewhere. It will be an enormously difficult thing to measure.