It would seem that they could, according to DGA rules, both receive a director's credit. Whether they choose to do so is apparently up to them. I may be wrong, but I think this site, like IMDb, relies on official credits only.

From Wikipedia:

"The rule that a film can only have one single director was adopted to preserve the continuity of a director's vision and to avoid producers and actors lobbying for a director's credit, or studios hiring multiple directors for a single film or television episode."

"The rule is waived only for directorial teams recognized by the DGA who have a history of working together and sharing a common vision. Examples include The Wachowskis, Jonathan Dayton and Valerie Faris, Hughes brothers, Russo Brothers, Phil Lord and Christopher Miller and the Coen brothers. . . . The Coens for years divided credit, with Ethan taking producing credit, Joel taking directing credit, and both of them sharing the writing credit (even though the two of them shared all three duties between themselves) until The Ladykillers in 2004."

I think this site, like IMDb, relies on official credits only.

Correct. We only support the original on-screen director credit. Determining who deserves the credit is the DGA's job, not ours.

The same is true for directors who are replaced (Bohemian Rhapsody) and rumored directors (Poltergeist).