That’s it in a nutshell, supply and demand. Everything is driven by supply and demand. And if you want any financial principle as the foundation for a (scientific) theory then this is it, just like we have conservation laws in the physical sciences.
Of course, quantifying this may not be that easy. Attempts to explain asset prices by modelling interacting agents have not been fantastically successful, whereas simply saying that the end result of all those interactions is a stochastic differential equation, has been.
I do sometimes wonder if the typical etiolated quant has ever been into a shop and experienced supply and demand first hand by buying a pint of milk. Whenever a quant calibrates a model to the prices of options in the market he is saying something about the information content of those prices, often interpreted as a volatility, implied volatility. But really just like the price of a pint of milk is about far more than the cost of production, the price of an option is about much more than simple replication. The price of milk is a scalar quantity that has to capture in a single number all the behind-the-scenes effects of, yes, production, but also supply and demand, salesmanship, etc. Perhaps the pint of milk is even a ‘loss leader.’ A vector of inputs produces a scalar price. So, no, you cannot back out the cost of production from a single price. Similarly you cannot back out a precise volatility from the price of an option when that price is also governed by supply and demand, fear and greed, not to mention all the imperfections that mess up your nice model (hedging errors, transaction costs, feedback effects, etc.).
Supply and demand dictates everything. The role of assumptions (such as no arbitrage) and models (such as the continuous lognormal random walk) are to simply put bounds on the relative prices among all the instruments. For example, you cannot have an equity price being 10 and an at-the-money call option being 20 without violating a simple arbitrage. The more realistic the assumption/model and the harder it is to violate in practice the more seriously you should treat it. The arbitrage in that example is trivial to exploit and so should be believed. However, in contrast the theoretical profit you might think could be achieved via dynamic hedging is harder to realize in practice because delta hedging is not the exact science that one is usually taught. Therefore results based on delta hedging should be treated less seriously.
To summarize: Supply and demand dictate prices, assumptions and models impose constraints on the relative prices among instruments. Those constraints can be strong or weak depending on the strength or weakness of the assumptions and models.