It's probably important to point out that there will be a difference between people running standard dwc versus systems that include waterfalls (which create aeration themselves) - you really want some form of aeration even if it's only some.
pH's rising are a common occurrence, even in chemistry labs, when you're trying neutralise / pH adjust something. They occur often where ever you have a large amount of 'stuff' present that you want to change the pH of. For instance, when you add pH down to your nutrient, the pH will rapidly drop. If you leave it and come back to check it hours / a few days later, it will have gone back up again. That's totally normal. It occurs because when you originally check the pH you are measuring the pH before the acid has had time to fully distribute and react with everything in the liquid. It's common for people to assume things are fully mixed when they actually aren't. There are ~ten trillion, trillion molecules in a lite of water. It'll take a while for all those molecules of acid to actually drift around and interact with the others. This creates the 'pH bounce' effect, where the pH rises when left (back towards neutral); as the acid (phosphoric) drifts around reacting with 'stuff' (nutrient molecules for example), it 'consumes' the acidity of the acid (alters it's polarisation). The good news is, it's totally fine and will stop doing it eventually; you basically need to just keep adding pH down a little at a time and it should level it's self out once it's all fully mixed and reacted (once it's polarised / unpolarised everything that can be polarised / unpolarised in the feed). It also shows people are actually checking their pH, rather than setting and forgetting.
As to why the effect might seem more pronounced with an air stone running, an explanation for that may be that you're actually accelerating the mixing process (pumping air into water shouldn't really noticeably alter it's pH a whole lot, especially if actual liquid form acid has been added to it beforehand). A significant benefit with hydroponics (of all forms) is at least the molecules can move around fairly fast by comparison with soil and you can easily empty it out; it takes a lot longer for solid material (e.g. soil) to actually fully react to a pH change.
In terms of pathogens entering the system via the air stones / lines, that's a possibility; it's definitely worth giving everything (including your hands) a rinse (soak the stone in peroxide if you want to be extra careful / boil the hydroton in pan with a lid on it and keep the lid on it until ready for use, then immediately cover it, with foil for instance, once in the mesh pots - keep your hands clean when handling it / avoid over handling it). You shouldn't really get substantial amounts of contamination through the air flow itself.
The air stone doesn't need to be directly under the roots if you have a flowing system, so long as the water is moving past the roots and past a bubbler (you can put it in the reservoir).
Something worth considering with air stones and pathogens is that, if the water is still, it will tend to stagnate; both biologically and in terms of its distribution. If you check out page 15 of
-> this link <- (the discussion section half way through on the left), they specifically mention controlling the mould
Phytophthora (which attacks plant roots) using the aerobic bacteria
Enterobacter aerogenes; it even has 'aero' in the name. The bacteria produces a form of exotoxin that appears to slow the growth of
Phytophthora. You'll need some level of aeration to keep it happy.
The air stone, regardless of it's size / throughput, also provides another function in typical dwc in that it disturbs the 'boundary / depletion layer' around the roots; if the water is totally stationary, the plant will gradually deplete the nutrient close to the surface of it's roots (any form of movement, even from a tiny air stone, will dramatically improve that).
I've tried fog-ponics. It seems to work fine for smaller plants but as they get bigger the droplets can't make it through the root bundles so easily. Whereas with dwc, the nutrient can more readily move around the roots.
People have mentioned that they would expect aeration problems early on in the cloning process if they were going to occur due to a lack of air stone. However, oxygen depletion and anaerobic stagnation take time to occur.
Electrolysis is a neat idea for oxygen generation in situ but be careful using it in any kind of enclosed space as it also produces hydrogen gas; so if it's left running for long enough (in a cupboard say, or recirculating in a bedroom, garage or loft) it could potentially explode when something switches on or off (the same is also true of storing some solvents in the fridge / freezer).
I'm not saying anyone is wrong (e.g. if you have a waterfall it should be fine), but I doubt it's a good idea in the long run to switch off the air stone on a standard dwc. Plants don't usually like growing around still water in the wild.