The speculation when it was announced LaFleur would interview for the HC position was that it was for a free consultation and outside assessment for the Titans, which is a tactic that is employed fairly regularly (or at least attempted) in the league now.
The Titans brought in a guy that hadn't called plays before, let alone lead an entire team. So he was willing to play the game because, at the very least, it gets his name out there among other teams and GM's in public. If he blows them away, maybe he gets the head gig. If he does really well, maybe he gets the OC position (which would still be a promotion for him, since he wasn't calling plays in L.A.) If he flops, then he gets to remain McVay's sidekick (or perhaps another OC job); but got a free trip to Nashville to gain interviewing and networking experience, while the Titans got, minimally, an outsider's assessment of their roster and ideas for future use of players.
I don't think the Titans were ever seriously considering him for the HC role, but he was impressive enough to get a true OC position.