One could say that to suggest that changing the apparent constants of our universe would make the universe we know impossible is an obvious tautology - if the constants were different it wouldn't be the universe we know. The weak anthropic principle may seem unsatisfying, but - unlike the fine tuning argument - it doesn't implicitly restrict complexity to the familiar. If, as seems to be the case, there is an action in low entropic states toward the maximisation of the rate of increase of entropy, then, statistically, the emergence of complexity (local complex systems) will be favoured, because such complex systems maintain their local entropy minima by increasing the rate of energy dissipation, so increasing overall entropy in the system as a whole. Increasingly complex self-sustaining systems (like life in this universe) would appear to be inevitable wherever they are possible. Whether such systems would become complex enough qualify as 'observers' is entirely speculative - they did here, but who can say what kind of complex systems might emerge in an entirely different universe?
In a pothole analogy, if you fill a pothole with a carefully shaped piece of wood and the pothole changes shape, the wood will no longer fit. This doesn't mean the pothole was finely tuned to the wood, it means the wood was tailored to that exact pothole; you could carve a new piece of wood to fit the new shape, and do the same for any shape of pot hole. However, that would be a design argument, and Occam might object. A liquid (e.g. water) is a more fitting analogy, it will match the contours of any pothole exactly without the need for careful crafting.