Dropping either side of a lateral hazard

This is Tecolote Canyon, the 11th hole.  The tee box is at the bottom right of the picture, the green is at the top right of the picture.   I went into the creek right at the bridge which is marked with red stakes.  My playing partner said there is a drop area on the other side of the creek.  The marshal happened to be driving over the bridge and I asked him if there was a drop area.  He said no.  I said, "no matter, it's a lateral I can drop on either side of the hazard no closer to the hole than where I went in".  He said, "no, you have to drop on the side that you went in".

It does make a difference as there are high reeds I would have to hit over and consequently I'd have to pick a club with enough loft that I couldn't reach the green.  I'm also planning on playing some course tournaments here and want to know the correct rule.

There are no local rules that are applying here.  I just think the marshal was wrong.

Was I correct?

You were correct. But would the point on the opposite margin of the water hazard be equidistant from the hole .

My understanding is I would have to pick the point on the other side that is of equal distance from the hole.  To do this I have to back up a few paces from where I went into the hazard.

BTW, that lateral hazard runs all the way back to the tee box.  However, for part of the hazard you wouldn't have the either side option as for maybe 3/4 of the hazard from tee to bridge there is no in-play area to the right to drop to.  The hazard is not all water, just a small creek in the middle of it.

I'm a little surprised too that the part that crosses the hole would not be marked yellow.  That is a classic candidate for being marked as red from the tee to about where the trees appear to end before the creek crosses the fairway, then change to yellow until it's across the fairway, then back to red for the remainder of the hole.

From what I'm seeing, it looks like the approach angle is better from the side you went in on anyway.  Not being on the ground there that's just a feeling - I could be wrong.

As far as the red vs. yellow... All I can say is it is a Robert Trent Jones designed course and I'll have to defer to his judgement (Assuming they didn't change it from what he originally designed.  If they did that would be sacrilege).

From the left side there are high reeds to hit over and with my line running just along the hazard I'd have to use a lofted club that couldn't reach the green or drop so far back that I'd be approaching with a 5 or 3 wood and would have to hit a fade.  Either way from the left side I still could mishit and go back into the hazard which is something that couldn't happen from the right side.  The right side is clearly the better side for me to play from.