While I agree with you in that this is an issue, it is in no way different from current systems. In current systems, stealing credentials of a bank give you pretty much enough power to move the money around. In the case of the LN, stealing credentials of a payment channel/tx gives you the possibility of compromising that payment channel, or to publish that tx.
However, the damage is not that bad if only one of the two participants is compromised:
In the event of key theft, the thief can simply try to cooperate with the counterparty in creating a new state that benefits the counterparty, creating some kind of LN-like protocol to ensure a part of the funds go to the thief. The thief must however do this for each of the channels and counterparties, while in the meantime the hub can update the state and invalidate the stolen keys.
In the event of tx theft, the thief can simply either publish a previous state (which the hub should have deleted completely anyway when updating), by which the hub loses all funds after counterparty proves fraud. Or instead, the thief can only publish the current state, in which nothing changes.
I do not really think this is much of a problem, but perhaps I am missing some case scenario here. Please complete my answer if that's the case.