If Riku didn't trust Sora, he'd sure as HELL be protesting Sora spending time with Kairi. But he did trust Sora. He DID. Maybe he didn't necessarily trust Kairi, but he trusted Sora. They really liked each other. They'd gone through a lot to get here. Riku didn't take that lightly.
"Oh Sora." Did he really have to ask? Riku went over and hugged him first. It wasn't like Sora was leaving... he was just hanging out with an old friend for the day. It wasn't unlike when Sora had class all day and they didn't get to see each other until after their classes ended.
"Invite her to dinner, okay?" Yeah, he was probably going to regret it later, especially if she said yes, but right now Riku just wanted to make Sora feel better.