It does depend
Only a chemist knows the answer and even she might answer, "It depends."
Joe Gores
I used to be a chemist, an analytical industrial chemist for Ferro Corp. (a US company actually)
so Joe your right the answer is "depends." (and I am only a she with a little wine and right set fo high heals)
What it depends on, and I insist that you count this as the official answer.
It depends on the thickness of the the Pure Aluminium layer on the outside of the sheeting, balanced by the corrosive forces the Aircraft experiences.
Protection
There is a layer of protection. It is Al2O3. This is EXTREMELY unreactive. It is what happens to pure aluminium when exposed to air. Not alot can react with it. So even a couple of nanometers of this will do.
Just right for it to go wrong
However if you scratch it, you expose the strength baring alloy beneath. No surface is perfect. Under a microscope it has natural variation. If at some small point you have a low point in the thickness of that protection, and that gets scratched then you will get corrosion from salts, organics, all that stuff. This is not a big deal and happens everywhere. It appears as a little pin prick of corrosion. If there is a high degree of salt exposure in an area where it stays wet to create the ion bridge that makes the whole thing work then that pin prick will continue to grow and will not stop untill
1. The water goes away
2. It hits something it can't react with any more (like the end of the part, ie its all gone)
So what do you do?
Do you know the level of integrity of the outer layer of Al2O3. That is the call that Cessna and Piper made. They also made this call. How long will it be before the thing coroded to a point of it being a probelm structurally. They made that call. I mean real maths, statistics, lots calculations, experiments, guys in white coats and clip boards ( I used to be one fo them ) then they looked at legal liability and the issue with reducing brand reputation if they get an issue. They then looked at how much it would cost to prime. ie Risk vs Cost
They found that with the quality of their Aluminium sheeting, with the mission of the aircraft, with the degree of corrosion, it would mean they could run the risk, considering how much it costs to prime, it was economically effective to not prime.
Knowing all of this, what am I doing
I am planning to fly my RV7 over big bodies of salt water. I am priming. If I was in the middle of Australia where its hot, there is bugger all water (not a lot) then I would make the call that the quality of Aluminium Vans uses is pretty good and it should be OK. You may get some spotting but the absence of water means the reation will be localised and won't eat your entire aricraft.
So.....?????
Where are you flying, how humid is it, how salty is it and how clean will the aircraft be on average. ... it "depends" on all of that
To all of that I would add this. How do you feel about not priming? How do you feel about the risk? Do you feel OK about it or do you feel not OK about it. IF your being honest about it, with information, your gut will make the right call.
That is my $0.02 worth.