Hi there. When I was growing up, one of my parents birds was a little goffin. He was ALWAYS (and still is) the "dirty bird". It's not that other, brighter parrots aren't "dirty", it just doesn't show up on them the same. If people comment that your bird looks dirty, tell them it's a sign you love him, because if he was trapped in his cage doing nothing all day long, he would be pristine white (which would be very sad for him). Just be sure he's getting regular baths, which may take a little training to get him happy about. Since he seems to be somewhat receptive of water, next time you give him a few spritzes, praise him and give him a treat. As he gets more used to it, extend "bathtime" until he's good and wet, and always be happy and noisy while it's bathtime to cue him that it's "fun". Also, I can't think of a single bird who would preen wet feathers. All my parents birds, as well as my own, will wait until they are dry to start preening (usually, they'll take a little nap after the excitment of a bath lol).
As for the "putting him on the ground" argument, I stand on the side that it's healthy and normal for birds to be exposed to a little dirt (use common sense). They certainly would be in nature, and just like in humans, it weakens their immune systems when they live in a sterile environment. Think about all the human kids who are getting asthma and autoimmune diseases and antibiotic resistance ect..., and all this is being caused by never being allowed to get near harmless bacteria their immune systems use as "practice". We oversterilize everything with bleach, antimicrobial soaps, hand sanitizer ect... (all nasty chemicals). It's not good for people or animals. Obviously, if you have other pets, lock em up when the bird is out on the floor. If you have pesticide treated grass, don't let the bird on the grass. Keep them out houseplants (even non-toxic ones) if they have been watered with fertilizer. All common sense stuff. But for the most part, it's just fine if your little guy wants to run on the floor, or outside (if hes clipped/harnessed). It'll build a strong immune system for him, and he'll be having fun exploring. My BFA had a repiritory infection when we first adopted him, but after he finished the antibiotics for that, he hasn't been sick since (5 years). My parents birds (all over 40 y/o now) have really never gotten an infectious illnesses (though there have been a few injuries, and had a stroke recently, but nothing germ related at all). All the birds in my family go outdoors (in the summer) and run free (including on the floor) in their respective homes. A little, normal dirt is far less of a concern with a parrot than using nasty chemicals around them (that will damage their tiny lungs) to keep germs at bay.
P.S. That's me with the "dirty bird" when I was about 2. He's such a little cutie pie. I really miss a house full of birds, but only have the time and space for my one special little guy

I hope in the future, though, to adopt a few more birdies!