For the millionth time in these forums. The price of BTC has absolutely nothing to do with the price of mining. The difficulty will adjust towards making mining a break-even venture. The difficulty rate lags the price due to the time it takes to bring miners on and offline. The price is solely determined by supply and demand.
The higher price of bitcoin brings in more miners, until the least profitable ones are at about zero profitability.
This means more electricity is used. In other words, total cost of mining goes up. There is a lag in this process, as you can't buy hardware in a minute.
Once more miners join, they all have to pay for their running costs in currencies other than bitcoin. That means they must sell their BTC on the exchanges. This creates a selling pressure on the exchanges, and keeps the bitcoin price in check.
So, yes, the price of BTC has absolutely everything to do with the (total) price of mining.