Are birds actually bathing when they flutter around in a birdbath?

Indeed, they are bathing. Birds have oil glands near their tail section. When you see them preening (cleaning and smoothing their feathers), it is to remove dirt and insects, plus spread the oil. A water source helps to remove any debris, which is why we witness them splashing about with wings extended.

They are splashing the water up under their wings and against their skin.

Yes, for all the reasons these guys above ^^^ have mentioned. We have a big, like 200 gallon rubber stock tub in our pasture by the fence line below our deck/driveway here and it is so cute to watch all the birds come to drink a flutter on the edge of the tub. Sparrows, bluebirds, flycatchers, doves, jays, robins, on and on. The squirrels drink from it too and who knows what all else at night.

It has an automatic fill when the bladder dips below the rim so it is always filled and we drain it and scrub it every so often. We also have mosquito fish in it. It is there for our horses and the neighbors cows when we have them over to graze on our big front pastures but mostly the wild life benefit from it the most. I love sitting on the deck and watching the birds drink and bathe.

@kritiper There is probably some truth in that. Birds do like a cooler water source during hot months, but the purpose for providing a birdbath is to provide clean drinking water and for bathing. The birds will dunk their head and splash the water with their wings onto their back. They will then fly to a nearby branch to preen their feathers.

@Coloma The tub sounds lovely. It also sounds too deep for the birds mentioned to bathe in. They need a source shallow enough for standing in order to take advantage of it more than a drink of water. I must be missing something based upon the description.

@Pied_Pfeffer They can dip and fluff but not a full bath like a birdbath. The little swallows skim over and splash though.