Can a bad alternator put too much juice to the battery, and causes it to die?

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Hi. So I was set to drive my brother's car back to Colorado from Oklahoma. He's stationed in Monterey at the moment. Needless to say the car that was in the hands of someone else ended in a bad condition. The steering is really hard and apparently I have an alternator that is putting too much juice to the battery. Which is causing the battery to die. And everything is reset in the car. it happened three different times. AutoZone tested the battery, and wasn't reading it as a full charge. So they took it in to charge. He came out to tell me the battery was leaking acid. But he was going to test if the battery is good or not. It was tested as good. The guy at AutoZone told me it is a bad alternator and I should obviously get it replaced. He said the alternator is causing the battery to boil over and pop those lids. An alternator can push too much power? Do I need a new alternator? Is that the issue?