In response to some of your comments, YES. I think peeing in the ocean is a perfectly acceptable thing to do. I mean really, if you can't pee in it, well, I said it just above. My problem is not with the ethical issues surrounding peeing in the ocean (do you move a standard number of feet away from the closest person, do you wait for a wave to come in, or go out, do you pretend to be just getting your hair wet, do you walk, do you stand still, does it attract or repel fish, etc.) but rather getting my children to quietly DO it. Because nobody wants to leave a nice spot like this,
spend an hour at the de-sanding showers getting rid of this,

and scuttle through rows of beach chairs holding scantily clad, impossibly tan women just so you can use a modern, but very damp toilet. It is a needless waist of time and exposure to pool feet fungus.
All it really takes is a quick trip into the ocean on one of these.

In fact this would have been a prefect time. Covered in salt water, an obliging wave veiling the face of the offender. It could have been so easy.

Or this. This is even better. A rush of water up to your waist. The pretense of playing in the waves. Again, so easy.

And yet, Matthew and Will both failed at their attempts (or rather my attempts to get them to). In Will's case the failure was mainly caused by fear. These waves were bigger than any he had encountered before and he was skeptical from the start.

He was not at all excited about getting in the water and completely content to stay on dry sand and annihilate his brothers' sand castles.

I tried explaining to him how much easier it would be to just wander out a few steps. How much time is would save. How inconspicuous it would be. I was so wrong. My dragging Will into the waves insisting he pee was not easy, did not save time, and was CERTAINLY not inconspicuous. Instead of quietly peeing Will took up screaming at the top of his lungs, "NO, in the toilet. In the toilet. NO, IN THE TOILET!" Okay, in the toilet. And to the bathroom we went.
Matthew's issue was not so much a lack of bravery as a lack of understanding. My instruction to run pee in the ocean did not bring tears, whimpering, or wailing. It sent a boy running full speed to the EDGE of the ocean, and there, backside toward a crowded beach, dropping his trunks. Of course, I caught him quickly and said unnecessarily loud, "Honey, come on now, we don't pee on the beach. Let's go up to the bathroom," my pleasant voice hiding the annoyance behind my eyes. After waiting a few minutes on our beach chair I returned to the ocean with him, carrying him in quite a ways and out of earshot of other bathers. But, in all the excitement Matthew just couldn't get himself to pee. As much as he had to standing on the dry beach 5 seconds before, once in the ocean with the freedom of a water cloak up to his middle, his giggly face and wiggly toes just couldn't relax.
So I gave in. We spent the time at the sand shower, traipsed through sun-bathing beauties, and braved the wet bathroom. But, we have many more summer days at the lake and will, for sure, practice up for next year.
p.s. I suppose I should confess, I don't have cute short brown hair nor am I a tall, beautiful red head. Those lovely ladies are my darling mother-in-law and sister-in-law. They were gracious enough to come on our trip with us and where great help and lots of fun!