Of all the possible criticisms for Vice President Biden to lob at President Trump in the closing weeks of the presidential campaign, the Democrat has settled on the complaint that the admissions policies at Mr. Trump’s country clubs are too restrictive.

“He’s the same guy who lets you earn a couple bucks parking cars at his country club, but even if you had the money, he wouldn’t allow you to join,” Mr. Biden complained about Mr. Trump during a September 30 campaign appearance in Johnstown, Pennsylvania.

In remarks the campaign had prepared for the candidate’s delivery at the event and distributed in advance, Mr. Biden said, “Look, I’ve dealt with guys like Trump my whole life. Guys who look down on you because they’ve got a lot of money. Guys who think they’re better than you. Guys who might let you park their car at the country club. But would never let you in.”

It’s a strange line of attack for several reasons. There is the novelty of the concept that blackballed country-club applicants nursing grievances are some kind of vast, previously undiscovered demographic category of swing voters. As if, in the midst of a pandemic, racial unrest, police violence, and substantial unemployment, what is really rankling undecided voters is that country clubs are stubbornly refusing to accept their initiation fees.

Any entry barriers that do exist have not impeded Mr. Biden himself. The Wilmington, Delaware News Journal reported in 2014 that Mr. Biden had joined the Wilmington Country Club. That club won’t let just anyone in; in 2001 it went so far as litigating a case involving a member, Louis J. Capano Jr., that it had voted to expel.

The Wilmington Country Club’s most recent tax return, filed in November 2019, reported that the non-profit, tax-exempt organization paid its general manager $435,234 in total annual compensation, its “director of grounds” $279,668, its “director of racquets” $262,808, and its executive chef $192,343.

The club’s 70-page rulebook makes clear that in the club’s dining room “jeans are never considered appropriate.” The club’s past presidents include William duPont Jr. A recent club newsletter advised existing members to search for the “next good member … individuals who you want to sit at the bar next to you.”

Nor is the Wilmington Country Club the only such institution frequented by the vice president. As recently as October 2019, Mr. Biden held a fundraiser at Fox Hill Country Club in Pennsylvania, where dues are $5,125 a year and there is an additional $1,000 annual food and beverage minimum expenditure for members. Photos of the event show an all-white audience.

The event cost $20,000 to co-chair, $10,000 to co-host, and $2,800 for a private photo with Mr. Biden, according to an account of the event in the Citizens’ Voice of Wilkes-Barre. The newspaper article indicates that, in his speech at the country club, Mr. Biden accused Mr. Trump of “abandoning the working class.”

Mr. Biden’s accusation that Mr. Trump is the one excluding people from country clubs is inaccurate. The reality is that Mr. Trump is the one who was himself barred from clubs in Palm Beach, Florida As a result, he started one with more populist policies.

Here is how the Washington Post, which is the farthest thing from a Trump campaign organ, described it in a 2019 news article: “Trump was shut out of all the private clubs, the heart of Palm Beach social life. … So Trump opened Mar-a-Lago as a private club in 1995. Unlike the Everglades or Bath and Tennis clubs, which did not admit Jewish members, and the Palm Beach Country Club, which admitted wealthy Jews, Mar-a-Lago was open to anyone. ‘Basically, he didn’t care who came in as long as they could pay for it,’ explains a Palm Beach social expert.”

The Washington Post article continued: “Trump’s open-door policy — his was the first club to accept African Americans and openly gay couples — began the slow process to diversify other clubs in town.”

It’s the same story in New York City, where Trump made money developing, managing, or operating mostly condominium buildings in Manhattan — apartments for people with money but without the references or pedigree or patience for co-op buildings and their arcane interview and approval processes.

As I wrote about Trump back in 2004 in The New York Sun, “There’s a contempt for Mr. Trump among certain of New York’s elites. He has unusual-looking hair and an unpolished New York accent. He’s highly leveraged, he’s in the casino business, he plasters his name on everything, and his family fortune was built on a lot of middle-income housing in Brooklyn and Queens. For an alleged billionaire, he seems to spend a lot of time either going bankrupt or narrowly staving it off.”

Mr. Biden’s attempt to portray Trump as some kind of old-money elitist is, like so much else about the Biden campaign, phony. If it’s the best Mr. Biden can do, the former vice president may find himself on Inauguration Day in 2021 watching the ceremony on television while drowning his sorrows at the bar at the Wilmington Country Club. Just so long as he doesn’t wear dungarees.