When Senator Scott Brown turned down an invitation to debate Elizabeth Warren at the Edward M. Kennedy Institute in Boston, did he shrewdly avoid a trap? Or did he foolishly blow an opportunity?

The invitation had been extended on June 8 by Vicki Kennedy, widow of the late senator and president of the institute’s board. Last week Brown agreed to take part in the debate – but only if Kennedy promised to personally uphold “the spirit of neutrality” by not endorsing any candidate or otherwise getting involved in the race. When Kennedy wouldn’t go along with that condition, Brown said no to the debate. “The Kennedy Institute cannot hold itself out as a nonpartisan debate sponsor,” Brown’s campaign manager insisted, “while the president of its board of trustees gets involved in the race on behalf of one of the candidates.”

To hear some Republicans tell it, Brown’s refusal was perfectly justified: Had he accepted Vicki Kennedy’s proposal, he would have been walking into an ambush. State GOP chairman Bob Maginn applauded Brown for spurning “this charade of a debate” and exposing the Kennedy Institute’s “invitation for what it was: a setup.” At the popular conservative blog Red Mass Group, Republican activist Rob Eno imagined a counter-scenario: Suppose Nancy Reagan invited President Obama to debate Mitt Romney at the Ronald Reagan Presidential Library in California. Would anyone fault Obama for declining such an offer?

It’s not a very convincing argument. The Kennedy Institute may be run by Democrats who idolize the late senator, but that hardly means it’s incapable of impartially hosting a political debate – a debate in which a Republican can shine.

And if anyone should know that, Brown should. When he first ran for the Senate 2½ years ago, the little-known state senator from Wrentham had no objection to squaring off against his Democratic opponent, Martha Coakley, in a televised debate sponsored by the Kennedy Institute and moderated by David Gergen. An ambush? It was anything but. The most memorable moment of the evening was Brown’s now-legendary retort when Gergen asked if Brown really wanted to sit in Ted Kennedy’s Senate seat and block health-care reform.

“With all due respect,” replied Brown, “it’s not the Kennedy seat, and it’s not the Democrats’ seat. It’s the people’s seat.” It was a pitch-perfect response, delivered with Reaganesque aplomb. It may well have been the turning point in Brown’s campaign. And it would never have happened if he had turned down the debate on the grounds that Vicki Kennedy might endorse Coakley. Indeed she had endorsed Coakley. What difference did it make?

Brown is one of the state’s most popular politicians, and is routinely described – even by prominent Democrats – as a gifted retail candidate. But this was a blown opportunity to reinforce what may be his strongest selling point with Massachusetts voters: his reputation for bipartisanship.

Brown touts his ability to work with senators on both sides of the political aisle, and there is evidence to back him up. An analysis of Senate roll calls published in January by Congressional Quarterly identified Brown as second only to Maine’s Susan Collins in his willingness to cross party lines on controversial votes: In 2011, CQ reported, Brown lined up with the GOP 54 percent of the time, but with the Obama administration 70 percent of the time. Using a different formula, the Boston Globe recently calculated that on the “most important, news-generating votes,” Brown has voted against the Republican leadership 24 percent of the time. “He has, in fact, demonstrated ideological flexibility,” observed the Globe.

Speaking at Bunker Hill Community College last month, Brown insisted that he is not the type of person “to divide people up into easy categories – assuming the best because they agree with me, or the worst because they don’t. Especially in politics, I’ve found it’s the only way to operate.” Brown could have strengthened that claim by accepting Vicki Kennedy’s invitation; turning it down only undercut the self-image he is at pains to promote.

To be clear, neither Brown nor Warren is refusing to debate: The candidates have already agreed to at least three televised face-offs, including one sponsored by a media consortium that includes the Globe. Nor is the debate over the debates likely to sway many votes on Election Day. But the episode is one more sad reminder of how easy it can be to view everything through a partisan lens, and to assume that the best gauge of someone’s integrity is the “R” or “D” after his name.

(Jeff Jacoby is a columnist for The Boston Globe. His website is www.JeffJacoby.com).