One possibility is that the White House feared that news of the hospital visit would leak out, prompting reporters to learn about the legally controversial surveillance program. A related possibility is that the White House specifically feared that the Democrats on the Gang of Eight, informed in some vague sense about Comey's objections to the surveillance, might have begun to raise private objections; leak themselves; or use other issues as a proxy fight against the secret program. In either case, it would make sense to bring The Hammer, who in March, 2004 was still powerful, on board to protect the White House.
There's no legal or Congressional requirement that only the Gang of Eight need to be briefed on such top-secret intelligence programs -- in fact, insufficient Congressional oversight was a main objection to the Terrorist Surveillance Program when Bush unveiled it in 2005. The trouble here is "it looks like a selective choice to brief political allies rather than a representative cross-section of congressional leaders," says Aftergood. Still, given that legal scholars consider the warrantless surveillance efforts to be constitutionally dubious, "it's probably the least offensive thing they've done regarding this program," he adds.
Bonus fun fact: the only other non-Gang-of-Eight members of Congress briefed on the warrantless surveillance were the heads of the Senate Defense Appropriations Subcommittee, on December 4, 2001. That's right, Democrat Daniel Inouye and... Republican Ted Stevens.
Update: This post originally misstated that Inouye and Stevens were, in 2001, the top Democrat and Republican on the Senate Appropriations Committee, when in fact they helmed the defense appropriations subcommittee. Thanks to reader GB for pointing out my error, which I regret.