In the case I witnessed, the happy camper arrived at a "nearly wild"campsite with only a hammock & Tarp. The site was near dartmoor on a slope leading down to a stream. Literally the only place with trees he could attach tarp lines to was in almost standing water near the stream, and it got even wetter over the weekend. I would have passed and found another site but he didn't, and made a pretty good job of it.
I managed to find a slightly raised bit of flat ground for my bivi and tarp set up and just about stayed dry, pretty much as Pattree suggested. Using a poled Bivi tent is actually no different.
Sometimes though, there is simply no choice in the matter, e.g. once at the old Bushcraft Show, very brambly and late arrivals had buggins choice. I was lucky and found the last flat'ish grass spot. Co-incidently the very same person arrived after me, and again ended up at the wet end of the slope, being the last pitch in the woods.
I do not plan to use that Nearly Wild site again though, even though the owners were lovely.