Does Aに助かりました mean that you were saved from A, or you were saved by A?
closed as not a real question by sawa, Troyen, jkerian♦, Tsuyoshi Ito, Dono Sep 20 '12 at 12:47
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助かる is an intransitive verb which means "to be saved".
Aに助かりました would mean "At the point of time/space of A, you were saved.(No agent is implied in the statement. It just means you were saved)"
Much like 窓が開く, it would mean "the window opens" without implying any agent.
Then consider ３時に窓が開く, it would mean "the window opens at 3 o'clock"
(Agent: one who initiates and/or completes an action or event)