Ken naturally disavows all knowledge of Tiffany until you can prove he knew her. This is more work for Joey, then.
After you leave the office, send Joey back in to snoop through the desk. Like Tiffany's mailbox, it's too dark to see, and there's no way to get a business card in there this time. The "dark shape" looks vaguely phone-like, though, doesn't it?
In the lobby, read the note on the right-hand door; it's from Ken and says he has Gal Friday's phone. So maybe that's what's in that drawer.
Look up Gal Friday and call the number, then send Joey back to look in the desk. The phone obligingly lights up when it rings so you can see that there's also a love letter from Tiffany in there. Ha!
Go back in and confront him. Keep talking until he repeats himself.