No offense intended
... to you or your wife by the question but to me the importance of "branding" is grossly exaggerated and I'm not the only one who thinks that way. Just look at what happened with the Kin - http://www.bnet.com/blog/salesmachine/how-kin-became-microsofts-worst-failure/10924 - all the Branding in the world couldn't save that failure.
Brand recognition and perception is initially and primarily developed by having a desirable product. The Brand is maintained, again, *primarily* through the product being of some acceptable level of quality and maintaining that desirable status. Good Brand management and recognition can help smooth over rough patches in quality like the examples you mentioned, agreed, but on the long term poor quality will tend to destroy a brand no matter how much is spent on marketing and advertising. I.E. you can only polish a turd for so long before most everyone realizes it's a turd.
I'm no Apple fanboy, but their products are seen by their clients as being of high quality regardless of their occasional (frequent?) issues with QC and I can't say that this is due *entirely* to marketing/advertising although possibly more than any other example, I would tend to say that they are a good example for how important Brand perception and recognition can be.
Don't get me wrong, please, I am not saying that the Brand, Brand Management, etc are unimportant. I have clients who live and breath by their brand and in the negative, and to your point, the brand *can* be everything. Your Brand perception being highly negative with your clients (BP, Goldman Sachs, etc) can really, really hurt you and potentially put you out of business... in which case rebranding to run away from your bad reputation might be advisable as I think someone else mentioned. That is, however, more of the exception than the rule.
More typically Branding attempts to polish/improve, or at least maintain the perception of a product. From that perspective it builds on the quality variable in the equation, but doesn't replace it.
And for the record, I'm not a Bill Hicks anti-marketing type.