The 139 was developed and marketed as a fully PC1 aircraft, including procedures and profiles to deal with that dreaded single engine failure.
On approach, the profile will settle you in a high vibration regime that could kick the AP's off. If you'd flown a 500 and instinctively minimized time in paint-shaker mode you'd be up in front of the FDM board explaining why you deviated from the PC1 profile.
I don't know Caverton's training, but likely focussed on engine failures (PC1 myopia). Not much time left over for AP's off, or standby instrument recovery from IMC. Not much different in the rest of the world.
I flew for a large operator that would regularly do both AP off training in the 139 aircraft, as did the factory. I noted other operators prohibited their training staff from doing this, citing a POH limitation.
Nothing like lifting off a deck at night with both AP's still off ....
I recall another highly-feted Nigerian crew ditching an S76 offshore after forgetting the AP's and deeming the aircraft too unstable to fly. Limited training time, focus on what the regulator wants to prioritize. In another case a droopy-eyed expat lost it in cloud between the beach and PH, saved by his sharp Nigerian national copilot.