As someone who has been de facto boycotting Apple (the last Apple device I've owned was an iPhone 3G) over annoyance with their iron fisted control policies, I wish you were right that this would damage their corporate brand, but I don't think it will.
Most non-geeks just don't care about this stuff one way or another. And most geeks either rationalize it or post how annoyed by it they are from their shiny new MacBook or iPhone.
I think this course of action is incredibly stupid of Apple regardless of public perception though. If they ever did manage to get Android killed in the way they seem to want to (Jobs' 'thermonuclear' option), don't they realize that would make them the 90's-Microsoft of smartphones? Is killing Android worth a future in which they have to cede control of the app store, debundle mobile Safari, or offer the user a choice of browsers, etc?
Given their corporate culture of control, having a relatively strong competitor is actually a VERY GOOD thing for them, especially when they are still pulling in record profits quarter after quarter even with the competition.
Of course, I don't expect they ever will actually kill Android, they are just guaranteeing Google is going to go after them in all the same markets using Motorola IP, forcing widescale settlements. In the end nothing will be gained by anyone except the lawyers.