What does “Barack Obama’s real crime is presiding while black” mean?

Question

I thought it’s unusual for me to be able to come to the end of Maureen Dowd’s’ article without any second thoughts on her particular turn of phrases when I’ve read today’s NYT article titled “Reindeer Games,” in which Dowd dealt with Michigan Congressman Kerry Bentivolio’s plan (or dream) to impeach President Obama for mishandling core issues from Benghazi to Obamacare to T.S.A. screenings. - http://www.nytimes.com/2013/08/25/opinion/sunday/reindeer-games.html?hp

However, I had a hiccup at the very end of the article:

“The Democrats never impeached W. and they had real grounds: starting a war on false premises and sanctioning torture. “The Republican Party is in a constant struggle between its ego and its id,” Axelrod says, “and the id has mostly won out lately.”

It isn’t the president who should leave. It’s the misguided lawmakers trying to drive him out. For some of the rodeo clowns clamoring for impeachment around the country, Barack Obama’s real crime is presiding while black.”

It sounds like it's saying GOP extremists think it’s a crime for a black person to be President.

Putting aside nonsense of the argument, how can I interpret “while” as a conjunction in the line, “Barack Obama’s real crime is presiding while black”?

OALD at hand defines ‘while’ as a conjunction meaning;

1. during the time that sth is happening.
2. at the same time as sth else is happening.
3. used to contrast two things
4. (used at the beginning of a sentence) although, in spite of.

Although I think the definition 1. applies to the above text, I’m not confident. Could you paraphrase “presiding while black” with more explicit or concrete wording?

By way of precaution, I’m simply asking grammatical and rhetorical interpretation of a word, ‘while’ used here. Please don't misunderstand. I haven’t the slightest intention to get into any of U.S related political or racial arguments.

P.S.

I found the article titled “Walking while black in the ‘White gaze’” in Sept 1 NYT, which begins with the following sentence:

“Man, I almost blew you away!”

Those were the terrifying words of a white police officer — one of those who policed black bodies in low income areas in North Philadelphia in the late 1970s — who caught sight of me carrying the new telescope my mother had just purchased for me.

“I thought you had a weapon,” he said.

I got a clue.

Answer 1

This is a reference to "driving while black", the term used to describe the "crime" for which black people are frequently pulled over when they are someplace police think they don't belong. Of course the police will claim they didn't come to a complete stop, failed to signal for a turn, drove too slow, etcetera. But they were actually pulled over either to intimidate them, harass them, search for drugs or contraband, and so on.

The use of the term "while" comes from the origin of the expression "driving while intoxicated", which was a reference to driving while under the influence of alcohol/drugs. Of course, "black" isn't a temporary state like "intoxicated". So it isn't a perfect grammatical fit, but it was intended to be ironic and darkly humorous.

The implication is that those who criticize Obama would do so no matter what he does as President because he is black and the specifics of the accusation are just pretense.