I think it's a calculated illustration. Power is all about making calculated gambles like that. If everyone was bare with their intentions all the time, it'd be easy for their enemies to bring them down.
The fact of the matter is that any type of change to the tax status of a significant asset is going to have far-reaching implications and plenty of people sticking their hands in the pot to try to make the outcome favorable to themselves.
A puff piece that features one of the most-conspicuous richest men in the world suggesting a tax hike against himself is just throwing a bone to the dogs; it's fodder that keeps Berkshire Hathaway and Buffett in the news and it makes the Buffett/BH brand more recognizable, likable, and personable, which are very important qualities.
It also gives him an anchor to point to if he ever needs to negate bad press. He can say "Look, I have a track record of advocating for selfless causes. What kind of greedy billionaire would get on TV and ask for a tax hike? You wouldn't see Donald Trump do that! The things that are causing my bad publicity are not actually bad, they're just misunderstood."
When people hear "tax hike" they think about it in relation to themselves, i.e., a hike on wage taxes. Beyond PR interest, the ulterior motives would be a) increasing the tax rate on people who are having good years in their small businesses, so that the growth of their nascent empire is stymied, lest it someday pose a challenge to BH's interests; and b) many of BH's major holdings are closely linked to government activity, things like railroads and utility companies. More money to the government = more money to BH, and this good PR makes government employees more favorable to Buffett/BH since he is not demonizing the thing that pays their salaries (taxes).
It's convenient to assume that people are honest and straightforward as long as one remains naive enough to believe that. But with something as complex and interconnected as BH and Buffett, nothing occurs in a vacuum. Buffett's private thoughts remain private. He knows when he is on the public stage and he certainly knows to calculate the consequences of his actions there. To deny that this is significant is to deny the purpose and value of Public Relations completely.