I can't really speak to BP's higher-level strategy, but this was the mid-2000s. The fact that an oil company was saying anything about climate change felt like a step forward. Other oil companies' ads were all about American workers and generic shots of sunsets over oil fields, BP wanted to position themselves as the "green" gas station at a time when that was becoming more a concern - not just with climate change but overall. At that point, BP had a pretty good environmental record compared to competitors like Exxon, who was still reeling from the Valdez disaster - so the requirement would've been to focus public interest on BP, not away from it.

But oil companies don't run ads telling people not to buy gasoline, so you've got to come at it from a slightly different angle. Luckily, "Greener than Exxon" was a pretty low bar, so they didn't need to talk about carbon taxes or emissions. Personal energy consumption has been a part of the discourse since the 70s, and probably fit in well - virtually no one will actually change their habits in any meaningful way, but will probably come out of it feeling better about themselves and BP.

The article itself seemed kinda all over the place. I agree that the world would be a better place if her preferences would've been enacted fifteen years ago, but I'm not sure that BP's advertising campaign had that much to do with it. It wasn't 4-D chess, it was "BP = Green = Good", and literally blew up in their face a few years later when Deepwater exploded.