You are wrong because you are thinking too much in terms of gold just because the word we use for both is the same ("to mine").

But what you are forgetting is that whether gold is worth one cent or a million dollar the cost to mine it is going to be the same simply because the process is the same.
However, this is not true about bitcoin. If bitcoin is worth one cent the cost of mining it is going to be proportional to that price, and if it is one million the cost of mining it will be higher to be proportional to one million dollar price.
This is one of the reasons that sets bitcoin apart from everything else. Bitcoin value is always defined by its utility and adoption. All you can say about mining is that it contributes a little to that value by providing security.

So you can't even begin to compare bitcoin's cost of mining with gold's and them create a correlation between bitcoin's value and that cost.