When Mark Zuckerberg told US senators yesterday (April 10) that Facebook is in an “arms race” against Russian trolls seeking to manipulate its users, his comment made global headlines.

One of the steps Facebook is taking to stop US elections from being manipulated by foreign actors is to put in place geographic checks—including literally mailing a postcard to an ad buyer’s address—to ensure that the money funding political ads comes from within the country.

Democratic senator Sheldon Whitehouse called out a problem with this plan, though: The legions of US shell companies that hide their ultimate owner.

In states like Delaware, Nevada, and Wyoming, a Russian citizen can start a company with few verifications (one academic study found it’s easier (pdf) to do this in the US than Panama) and register it in the name of someone who’s a director in name only and has no visible stake in the company—while actually owning it via a foreign tax haven.

As Whitehouse put it, “If they were running through a corporation domiciled in Delaware, you wouldn’t know that they were actually a Russian owner.”

Zuckerberg had no quarrel with the argument. “Senator, that’s—that’s correct,” he said.

Whitehouse has co-authored legislation that would put a dent in America’s slide toward Switzerland’s place as the world’s number-one tax haven, with a simple step: force all companies to tell authorities who owns them. That wouldn’t make it easier for Facebook to trace whether Russians are actually paying for political ads, since that information is only available to law enforcement, but it would make it much easier for authorities to catch them for illegally contributing to a political campaign.