why is double-spend not an issue for payment channels?

Micropayment Channels (MPC) cannot be used currently because of transaction malleability, I hear.

AFAIK, people saying that have in mind that the refund & payment tx, which have as input the deposit tx (Dtx), could be invalid if the deposit’s hash was changed. I m fine with this.

What I don’t understand: if the attacker manages to modify Dtx’ hash before it made it to the blockchain, I believe (s)he can equally manage to double spend the btcs supposed to go to Dtx. Thus, double spend seems as much a threat as malleability. Yet no one discusses it, so I suppose something is wrong with this reasoning. What?

Thanks

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