That's kinda how their website puts it. But I just was there, brought in a 32oz. Powerade bottle refilled with water in my hand. Security people didn't say a thing. I thought If they said no I would pore the water and refill it in the park (even though the water there is nasty). So take a chance. If you have kids I'm sure they wouldn't stop you.
Yes, you can bring in bottled water
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