No, your logic would only hold for a public company with shares priced by a liquid market.
For a startup, percent ownership of fully-diluted shares is the key metric. (Other secondary factors, e.g. liquidation preference are also relevant.)
The strike price of the options is derived from the price that the most recent lead investor paid for the last shares purchased. This is not a market price -- the underlying value of the shares is often less.
But the options are effectively worthless until they are vested and a liquidation event, usually an IPO or acquisition, occurs.
