A lot of this hinges on what you mean by 'flier'.
Many people use it to mean any shot that appears not to be grouped with the rest. So with 3 shot groups, where the 'two together and one apart' pattern is very common, people often describe the one apart as a flier. As my simulations should show, it's not - it's a common outcome of random sampling from a normal distribution.
As you suggest, another (and probably far more rigorous) definition of a flier is one that sits >2SD from the point of aim. Though remember we're dealing with a distribution where the mean is 0, with a symmetrical error either side of that. In very simple terms, assuming we're only thinking about error in the vertical component, our -2.25% goes low and your +2.25% goes high.
The reason we over estimate accuracy by being more willing to accept 'good' groups as evidence of an accurate rifle is this: with any normal distribution, you do still get a 'lump' in the middle: you are more likely to see a shot close to the mean than one away from the mean. So a while a true 1MOA gun is very unlikely to produce a 2MOA group, a true 2MOA gun can still produce 1MOA groups.
The plots below should illustrate this. They show how often a shot falls a given distance above or below the point of aim. Blue is from a 1MOA gun, red from a 2MOA gun. As you can see, for the 1MOA gun, the likelihood of seeing a shot more than 0.5" above of below the target is vanishingly small. By contrast, the 2MOA gun still gets a fair number of shots within 0.5" above or below the target.
View attachment 401510
I think this means that when deciding if a rifle is accurate, the question should not be 'can it shoot a 1MOA group'. It should be 'what is the largest group it shoots, over n shots under optimal conditions'. You then decide what n you're happy with. For most of us, that seems to be 3! I reckon for stalking purposes, 20 is probably enough. At least you'll get some practice while doing it.
