Those seem to be several questions at once.
Physical strength has both a neurological as well as a morpholocical component (1). It is true that resistance training allows you to activate a higher percentage of your muscle fiber ("Neural Adaption"). However, actual strength, as in being able to move heavier loads, depends on the absolute amount of activated muscle fiber. This is the morphological part of strength ("Hypertrophy"). To display the maximum amount of strength, you need to have both much muscle tissue and also be able to recruit a high percentage of it.
As a matter of fact, neural adaption takes place a lot faster than building additional muscle tissue(2):
This is why you'll notice an incredibly quick rate of progression despite not seeing any changes on the weight scale when you start to regularly work out for the very first time.
In a way, individual maximal strength is indeed limited by one's genetic potential. But the difference in peoples' potential mainly stems from the body's response on training in terms of muscle mass (3).
Regarding obese athletes - These usually compete in the highest weight class of their sport. This is because the additional fat doesn't impede your performance (bench press), or even has a slight beneficial effect (squat, snatch) (4). Looking at the other weight classes, you'll barely see anyone seriously competing with a bodyfat above 15%, as the ability to compete in the lower class strongly outweights (no pun intended) the benefit of extra fat tissue.
(1) Folland, Jonathan & Williams, Alun. (2007). The adaptations to strength training: Morphological and neurological contributions to increased strength. Sports medicine (Auckland, N.Z.). 37. 145-68.
(4) Why is it beneficial for powerlifters and heavy weight olympic lifters to not have low body fat?