How do you know he didn't piss into it? They usually piss all over their leg so it runs down over their tarsal glands, you might not notice this from your vantage point. It's not usually a stream like us!
I suppose you "might be right.....but I was 9 yds from the one I saw the 4 work, that morning....and I think I'd have seen it (could be wrong).
I've also been fortunate enough to witness a doe peeing on her tarsals.....and a "stream" it was. It was the goofiest thing I've seen a deer do, in person. She was at it for quite a while.