Take a look around the political Web today, in the wake of Tuesday’s primary and special elections, and the consensus seems pretty clear: incumbents, insiders, and assorted other establishment types, run for the hills!

The New York Times has been reading lately as if reporters are under a style directive to use the phrase “anti-incumbent wave” as often as possible. Meanwhile, in their lead story, the meme-setters at Politico argue that the incumbents are imperiled not so much by broad-based, swing voter anger but by the rising power of political activists. As in most of today’s coverage, Kentucky and Pennsylvania get the starring roles, but Arkansas—where the closely watched Democratic Senate primary between Blanche Lincoln and Bill Halter produced an inconclusive result and is headed for a run-off—is slotted into the framework too:

In effect, the anti-institutional forces that coalesced in recent years now look like an institutional force of their own.

They beat incumbent Republican Sen. Bob Bennett earlier this month in an intraparty battle in Utah. They beat once-safe Democratic Rep. Alan Mollohan in West Virginia.

And on Tuesday night, liberal activists forced Democratic Sen. Blanche Lincoln of Arkansas into a run-off as the two-term incumbent failed to even come close to the 50 percent threshold needed to secure re-nomination against challenger Bill Halter.

There’s clearly something to this. Halter’s campaign did rest on a foundation of financial support from activists like the liberal “netroots” and labor unions who had targeted Lincoln not just because she was an incumbent, but because she was an incumbent who did not support their views on key policy disputes. And those activists got involved on the challenger’s behalf despite the stated preference of the Democratic establishment, including the president, for the incumbent Lincoln.

But a closer look at the results in the Razorback State offers a more complicated, more interesting story—and suggests we should, for now, avoid sweeping claims about yesterday’s vote, who’s favored in the June 8 runoff, or how the race fits into a larger narrative.

For one thing, consider that Halter’s political identity, and his base of support, may be quite different within the state and outside it. Nationally, he’s the candidate of the progressive base, and when veteran Arkansas journalist John Brummett talked to CJR a couple weeks ago, he saw Halter making inroads in liberal-leaning areas like Fayetteville and Little Rock. But, as it turns out, Lincoln polled over 52 percent in both Pulaski County, home of Little Rock, and Washington County, where Fayetteville is located, compared to 45 percent statewide. (See Politico’s very handy interactive map for details.) Here’s how Brummett described the results:

…the remarkable thing is that rural conservative voters across southern and north-central Arkansas went for Halter, surely out of animus for Lincoln or incumbency or Obama — or in a backlash against Lincoln’s late embrace of Obama to make a play for black and liberal votes — and without any awareness or consideration that Halter is the candidate of labor and national liberals. The gap between MoveOn.org and such Arkansas counties that went for Halter as Grant, Little River, Van Buren and Baxter is vast. Halter appears to have gotten a near-equal share of the Delta black vote, too.

That “surely” may be a bit much, but the broader point about the gap between Halter’s national backers and his local voters is valuable. Max Brantley of the alternative Arkansas Times was also struck by the geographical breakdown:

Subtract Pulaski, Washington and Benton county votes and Bill Halter led the Democratic ticket. To generalize, he scored strongly in rural areas, carrying a number of counties in, for example, the 4th District [in the southern part of the state]. I don’t think this was, despite what the national press would have you believe, a liberal uprising. (Do you, Mike Ross?) The vote was anti-Blanche…

Greg Marx is an associate editor at CJR. Follow him on Twitter @gregamarx.