No really. the main reason is the betting on futures that is driving up the costs on oil, this ponzi scheme is also in place on pretty much any commodity that gets traded today. Check out the gambling that have been driving up the price of wheat and oil.
And the fact that the dollar gets low or high have no relevance for the oil price since prices are set in dollars in the first place it doesnt matter if it goes up or down.
For the rest of the world that uses oil for fuel etc ( which is most of it) the fact that the dollar is weaker means oil prices have gone DOWN, price at the pump is lower than it would be if the dollar was stronger. That right there proves it has no connection as you say it does. Since really if the dollar value being lower makes the gas cheaper in Sweden and a strong dollar means the cost is going up.
Look on this as 2 sliding bars dollar value on one of them and oil price on the other prices changes based on where those bars are but the value of the dollar have no bearing on the cost of oil if it is your own currency since you are by default insured against exchange rates since you deal in your own currency.