The functional fitness craze does enhance core stability which in turn will lead to a flatter stomach simply by virtue of it being partly tensed all the time.

To get a “Men’s health” body requires a LOT of resistance training and a superb diet…. otherwise called bodybuilding. A “lean ripped physique” and “beef” are not mutually exclusive things. A model like the ones you describe has plenty of beef, he just has very little fat… not so little as a stage competitor you understand, but well below the magic 10% barrier.

These trainers, and I use that term loosely (the vast majority of personal trainers I meet have very little idea of what they speak, despite their qualifications) are simply trying to line their pockets by playing on the general ignorance of the population when it comes to fitness.
You can have the best trainer in the world at the gym, but if you have a shit diet, then you will never get that model look.

That said I can understand why you may want a break from traditional training so the best thing you could do is what we term strongman type training where you basically throw, lift, drag, and generally move heavy objects for short bursts of time (sub 30secs) with 60 secs rest between sets. Its brutal and can be great fun.

I was working at Leicester Tigers rugby club recently and we were flipping tractor tires, dragging sleds and throwing heavy bags. People were dropping like flies it was so tough, and the following day my biceps were so sore they felt as though they had been tenderised with a baseball bat!