The issue has been acknowledged by Christian Svensson at Capcom, who stated that Capcom has no plans to patch the feature in, and that its inclusion in the manual was a mistake. "The reason for this difference is because of the architecture differences between [Xbox Live] gamertags and PSN IDs. I'm not sure of the technical details, but basically it amounts to: Sony made it so you can mix and match online and offline, and Microsoft made it so you can't."
That sounded like a reasonable explanation, until we remembered that the 360 version of Mortal Kombat does that exact thing, allowing two local players to take part in tag-team battles online. If it's possible for NetherRealm Studios to include the feature in Mortal Kombat -- the MK studio's first release under the NetherRealm banner -- its exclusion from Capcom's brand-new flagship fighter seems strange at the very least.