What does it mean?

What you find in America is that certain drugs approved by the FDA are sometimes kept from the market, not for safety reasons but for political reasons.

There was recently a dust up over the FDA recommending that "Plan B" (the morning after pill) should be available over the counter (without a prescription) to anyone who wanted to buy it. Many anti-abortion politicians didn't want this to happen and the decision was overturned for political reasons. (Here's one news story about it: http://www.nationalreview.com/articles/286073/sebelius-and-plan-b-kay-hymowitz)

The writer of your article is suggesting that these decisions should lie solely within the scope of the FDA.

I'm not really sure. I think I'd have to see more of the article. (Your "more" doesn't have a link following it.) I need to know what precedent they're discussing.

I think what they mean is "not just with a cabinet secretary but with the President himself".

I think your "or" would be wrong. They aren't saying that it would be the secretary OR the White House, they're saying it would be the White House, not the secretary.

The Secretary is not an elected position so they might not make the most politically expedient decision.