"We do not make decisions based on petitions," the Trader Joe's statement reads. "Recently we have heard from many customers reaffirming that these name variations are largely viewed in exactly the way they were intended—as an attempt to have fun with our product marketing."
There are three ideas in the above and as far as I know each one on its own seems to be true. But it doesn't take much to see that each statement alone doesn't speak to any relevant concerns raised by the petition:
(a) I'm not aware of anyone accusing Trader Joe's of making decisions based on petitions.
(b) I don't expect people offended by the branding to have remained customers, which means they probably aren't contacting the company with their support.
(c) The petition wasn't a critique of the original intent.
In other words, the quote takes sentences that each serve a different point and brings them together as a response to the petition. At best, it's an indirect acknowledgement of the concerns; I like to think that the remaining space was filled by my original post.
One thing to note about this strategy is that you'll see it all over politics. I often notice the construction whenever I disagree with someone; I'm so certain of my objection that I'm stunned to find a sea of facts in the transcript. It's sometimes amusing to me when politicians are called liars, because it's a futile exercise; politicians don't really lie, they speak mostly in facts, which their supporters need in order to justify their positions.