When viewed within the context of the entire song, it is the narrator asking Northerners if they believe they should all be judged based on Nixon's actions, as they judge all Alabamians based on George Wallace's. It was really an answer to Neal Young's songs "Southern Man" and "Alabama."

Sweet Home Alabama was written from the point of view of a man from Alabama (but it could be any Southern State really) who thinks they are all getting a bum rap based on the actions of their leaders (George Wallace, Ross Barnett, etc.). The line immediately preceding the Watergate reference is:
"In Birmingham they love the Gov'na (Boo Boo Boo). Well we all did what we could do."
Van Zant (speaking as the Alabama narrator) is saying, "look, there are a lot of us that don't like him (thus the booing) and we tried to get him out of office, but it didn't work. We aren't all like him." And in the next line, he's asking "Do you feel guilty over Watergate? Should we judge all of you by what Nixon did? Are we supposed to think you're all like him? If not, why do you assume we are all like Wallace?"
It's very subtle writing and has been misinterpreted by detractors and fans both.

I heard pretty much this type of comment very frequently back in the 1972 - 1974 timeframe. Today I still encounter people who think that Nixon was unfairly railroaded.

This is anecdotal, but I remember the Watergate era very well (better than I can remember what happened last week, sometimes!). But at that time, there was a cultural war going on between the pro-establishment public (those whom Nixon called "The Silent Majority") and the emerging youth/counterculture (championed by George McGovern in 1972).

There was massive civil unrest in the US unlike anything the country had seen since the Civil War. The Kennedys and M.L. King had been killed, and the majority of Americans thought these were the acts of political conspiracies. Riots and protests were common. The 1968 Democratic Convention was marred by bloodshed committed by the Chicago police against primarily youthful protestors. There was a million-person protest in Washington DC (the "War Moratorium") that practically shut the city down. There were countless bombings, active domestic terror cells, and even a rash of airplane hijackings. US soldiers had committed unspeakable atrocities in Vietnam (Mai Lai, etc.). Unarmed college students were shot by the National Guard at Kent State (which Neil Young sang about, at about the same time period he sang about Alabama in "Southern Man").

Many conservative people, took the attitude of something like, "my country - right or wrong". These were the people who were proud of the US victory in World War II (and, they thought, Korea). There was a strong sense of 'realpolitik' regarding the ability or necessity of the Government to do unpleasant/dirty deeds in order to maintain order in society. The Watergate burglary had been made public a couple of months prior to the 1972 Presidential election, and yet Nixon won in an overwhelming landslide over McGovern (taking 49 out of 50 states), and by proxy, the entire counter-culture movement. So there was a very strong backlash against the counter-culture movement. And many, maybe most, Americans were not very worried about a little burglary when faced with impending anarchy.

Also, that was the time when Nixon masterminded the "southern strategy" whereby the Republican Party took the Southern states away from the Democrats. Ever since the Civil War, the South firmly supported the Democratic party. After the Civil Rights movement, and following the resurgent 'conservative' movement led at first by Barry Goldwater (followed by Nixon and then Reagan), the White South started backing Nixon and the Republicans. Lynyrd Skynyrd's lyrics reflect this attitude.

I believe the tide against Nixon turned during the televised Watergate hearings. On a daily basis, people were finding out that nearly all of Nixon's staff were, indeed, 'crooks' and many of them were packed off to jail. And, when the transcripts of Nixon's Whitehouse tapes was released, people for the first time were exposed to the private Nixon. The private Nixon was a foul-mouthed Machiavellian racist, as is evidenced by what the tapes revealed. That was when, in 1974, even avid Republicans turned against Nixon, and his own party voted with the Democrats to impeach him.