Err, the notion that people who lug heavy objects around like fridges must by definition be weightlifters is incredibly dodgy. Strange though it may seem, people can develop great strength without needing to do artificial weightlifting of metal dumbbells. You have to bear in mind that for millenia beforehand, people were exposed to regular stresses such as pulling ploughs through hardened soil most days etc.
you are still majorly distorting the definition of strength if you are referencing martial artists. Once again the subject is 'how big', obviously its not talking about some master of reality that can kill a man with his pinky, this is not strength.
here is the world's strong man competition
http://en.wikipedia.org/wiki/World%27s_Strongest_Manyou can see that there are many exercises that are extreme versions of what has been labeled 'functional strength exercises'. There is absolutely no way that an everyday person of any time period incorporating resistance into their daily routines no matter how arduous would ever have a chance in these competitions, same with any martial arts master.
In order to build serious strength and size, you need to continuously stress your muscle groups. This cannot be accomplished simply by everyday activities no matter how stressful. You can do this 'functional strength training' by using some kind of natural object in combination with movement which might make up a huge piece of the puzzle but still won't make a difference unless you do something artificial like change the weight over time. Without using any kind of weight you are in the dust as far as putting necessary strain on your body.
I worked for 2 years moving insanely heavy objects which involved lifting, pushing and pulling. I didn't leave this experience particularly bigger or stronger. My boss had a freakish ability to just throw things around like they were foam, but he lacked any real muscle definition and no one would ever look at him and say he had a strong build.
the subject is how to build strength and size. you can express your preference all you wish about effectiveness especially in fighting but strength as defined by a normal person includes in all cases ability to move weight from point A to point B. If one is doing various bodyweight and functional strength exercises, and CANNOT compete in lifting isolated weight in a non complex circumstance, their routine is clearly not as efficient in building strength. If the weight trainer can't do simple feats like pull-ups, I can guarantee they are not in the world's strongest man competition and I can guarantee all of these men incorporate weight training into their routines.
Ironically I prefer a smaller more efficient build myself, and I do body weight training and almost no weight training. But in usefulness to others, I recognize that I can fine tune my routine and push myself to the limit and will never have massive strength or size. If one has a goal of serious size and strength (the ability to lift a giant weight if necessary) they will do much better in time with weighted exercises, I can say that 100% with experience and confidence.