In this trailer of Frozen 2, there's this line:
00:46 OLAF: I’m gonna blow!
00:47 KRISTOFF: I got you.
It sounds to me more like "I've got you" but the subtitles say it's "I got you."
Regardless of what he actually said, are both possible in this type of context? If "I got you", but not "I've got you", is possible here, what's the reasoning for that?