Not knowing the full details, it wouldn't surprise me if the following combination of events took place:
- The plane was at (or over) gross
- It was a really frickin' hot day
- The plane was at low altitude when the engine failed, not providing much time for reaction
- The pilot didn't respond properly
With full fuel, I can still put 1200 lbs in my Aztec. 6 people and luggage pretty easily meets or exceeds that (when we've done 6 people, I was the only male in the plane). The plane will not climb particularly well at that weight on hot summer days, and you'd need to be at around Vy to get a good climb rate. If they were over gross on a hot day at a relatively low airspeed and not much above ground, I could easily see their result happening.
I rarely fly near gross. Even when I did my Mexico trip and had three humans, luggage, survival gear, and 9 dogs heading to Colorado, we were a couple hundred pounds under gross, improving as fuel burned off. I have tested and, if flown properly, my Aztec will maintain altitude just fine with the left engine dead and the airplane clean at gross at or below about 6000 ft MSL on a hot day. However if one had failed on me right after taking off from Cozumel while I was still at low altitude, low airspeed, and climbing, it would definitely be work to get me back to the airport. I'd first fly out over the ocean to try to regain some altitude, then come back in. It'd be doubly hard if it was the left engine and that meant I lost my hydraulic pump and would have to pump down the gear manually (fortunately in that case I had a co-pilot who could have helped).
While this isn't the Aztec below, piston aircraft CAN cruise on one engine if flown properly. The below picture was taken on a hot day with full fuel, although still well under gross. I landed it with the prop like that. It was only a problem once I landed as that particular plane didn't want to taxi on the right engine only (Aztec will) and I had to mess to restart a feathered engine on the ground before continuing.
One more point: I do a good sum of single engine training in twins I fly and am a big believer in it. While I generally don't actually feather the engines, I will pull the power back on one engine once a safe altitude has been reached and do my various maneuvers to remind myself how the plane flies in the degraded mode. My takeoffs are done with the assumption that an engine WILL fail at any point in the process, and so I take precautions to give me the best chance of success when that happens. Will it work? Beats me, I hope to never have to test it.