^^
How about this.
You live on a station where people get taken over by evil entities once a week. You served on a ship where you yourself were taken over by an evil entity. It happens. You're aware of this.
A good friend shows up, yells at you about something that never happened, and you just say "You're right" and move on? Or think "Hey, something's not right, me and Will left on great terms, he's lying, I'm warning someone NOW." At least, if you're as experienced as O'Brien, you'd think you would. Step off the Defiant, hit your badge (it's really convenient) and say "Sisko, there's something up with Commander Riker, he's on the Defiant..."
Easiest solution, as pretty much stated before, would be Tom saying "O'brien, great to see you, let's catch up at Quark's tonight!" Then move on. Takes the same amount of time. And it isn't stupid.
(laughs) If I "hit my combadge" every time people acted in a way that I thought was unusual and not necessarily consistent with what I knew of them, I'd likely be in an asylum by now. Usually I respond with an "Oh...okay," and file it away for later analysis (i.e. I'll ask other people who also know the person whether anything's going on).
It's also a bit of a stretch to claim people got taken over by evil entities once a week, but I suspect you already know that.
In any event, matters progressed so quickly that even if O'Brien did with relative haste decide this constituted a problem and pursued things, it was probably already too late. How much time elapses from that conversation to the Defiant's departure? 5 minutes?