I don't think there's any reason to believe they can't have their own rules in this regard - especially since senators in particular represent the state itself and the United States is (was?) a federation of the states, therefore the states technically have (had?) the power over the feds and not the other way around. Sending representatives from each state is (or should be) the state's privilege and should not elevate them to king-hood over the very state they are supposed to represent the interests of.
Of course.. it's never been tested because a recall attempt of a US Senator in any state that allows for it has never progressed to the point where it'd have to have been implemented and so it may ultimately be illegal if the supreme courts says it is. However states have a certain right to withdraw from the union as a whole because of disputes like this because the union itself exists at the request of the member states themselves. We at least know that has been tried, but it didn't go very well...
Of course.. it's never been tested because a recall attempt of a US Senator in any state that allows for it has never progressed to the point where it'd have to have been implemented and so it may ultimately be illegal if the supreme courts says it is. However states have a certain right to withdraw from the union as a whole because of disputes like this because the union itself exists at the request of the member states themselves. We at least know that has been tried, but it didn't go very well...