In fact, while Palin's Fox riff was a smear (impugning Obama's motives with no factual basis) it did not include an actual lie -- she didn't say that Obama got more money from the oil industry than any given Republican. In elusive, allusive convoluted fashion, she piled hypothetical on hypothetical. After asking why the media doesn't ask "if there's any connection with the contributions made to President Obama and his administration and the support by the oil companies to the administration" (literally, a connection between the oil industry's support for Obama and the oil industry's support for Obama, but you know what she meant), she goes from speculation about what is (or could be) to counterfactuals about what might have been or could yet be:
now, if this was President Bush or if this were a Republican in office who hadn't received as much support even as President Obama has from B.P. and other oil companies, you know the mainstream media would be all over his case in terms of asking questions why the administration didn't get in there, didn't get in there and make sure that the regulatory agencies were doing what they were doing with the oversight to make sure that things like this don't happen.
Palin seems to be dreaming up a hypothetical Republican who hasn't been massively supported by the oil industry. We are literally in fantasyland, where it's natural to body forth the possibility that Obama has been influenced by oil money and then conjure a Republican president who's received "even less" than Obama but whom the media will assume (as it would have with Bush, who received proportionately more of the industry's dollars, but never mind...) is more influenced than Obama is (was). And just as the slip about "support by the oil companies to the administration" suggests the opposite of what she purportedly means, so the "even" in "even as much," taken literally, would seem to suggest that Obama hasn't received much from the oil industry. Palin gets lost in her own funhouse.
Moreover, the smear about Obama going soft on his alleged benefactors borrows a ghost of plausibility from the fact that what Palin says about how the media would respond to a Republican president in Obama's shoes is true. Media would assume undue industry influence on a post-W. Republican President. Indeed, media do assume, I trust, that the Bush administration, e.g. Cheney, made the Minerals Management Service (MMS) a toothless, corrupt shill (or even more of one than it had historically been), and that the Obama administration hasn't gotten around to effectively reforming it yet (UPDATE: today the Times, reporting a new Inspector General's report spotlighting MMS corruption from 2005-07, asserts: "Industry watchdogs say that much of the inappropriate behavior found by the Office of Inspector General had stopped with the new administration. But some repercussions continue.") Who, knowing anything about Cheney and Bush's industry ties and avowed Republican policy of selling legislation to the highest bidder and putting industry lobbyists in charge of regulatory bodies -- or who had heard of the Inspector General's 2008 report painting MMS as a sink of bribery and adultery -- would assume otherwise?
Equally interesting is Palin's fantasy view of the power of heads of state. Her excoriation of Obama "taking so long to get in there, to dive in there" recalls her memories of when Vladamir Putin "rears his head" and flies into American airspace. Heads of state are superheroes! And so is Sarah.
Does the expression of these weird fantasies on a national stage matter? Yes.