... but it can act as a floor (elastic lower bound) to the price during down swings. ...
If the value of a bitcoin drops, then people stop mining and that lowers the cost of mining. In other words, if the price drops, then so does your "floor".
Even so, people would still select the cheapest means to get coins. Investing in mining rigs is an efficient way, so we did not see a lot of buying order on market (the capitals went into mining devices). But if difficulty rose to a level that investing in mining rigs will bring almost no return, those investors will back to exchange and buy coins
If more people start mining because it is cheaper to get coins that way, then the cost of mining goes up until it is no longer cheaper. I'll concede that there might be inelastic responses or inefficiencies that temporarily cause the price of a bitcoin to be influenced by mining cost. But overall, mining cost is determined by the price of a bitcoin and not the other way around.
And just like marcus_of_augustus said, the cost of mining act as a reference of the coins exchange rate (if the cost is higher than price of the coin, miners will shutdown rigs and buy coin directly, their buy will raise the price)
If miners stop mining and buy coins directly, then it makes obtaining coins through mining cheaper. The two must cancel each other because the demand does not change. The supply is unaffected, so the price does not change.