One more than I've seen. Again, aside from Red Gyarados, I played through both Silver and Crystal in addition to the above-mentioned.
The point is, it's not impossible, and it's not cheating. I'm not trying to change your mind and make you hump Hidden Power like a love doll, I'm just saying that calling someone who did the work and effort to get a Hidden Power Ice on their Raikou or Infernape isn't a cheater and not some dick move they did.
It is not impossible, my point this entire time has been probability, and I apologize for generalizing in my earlier posts. But it is EXTREMELY unlikely. And I don't think you realize how ridiculously common Hidden Power is in competitive communities, and that's solely because they were all "raised" on NetBattle. Go into any competitive guide such as Serebii's Pokemon of the Week, and barring an "uber" TM pool, virtually every Pokemon with a viable Special Attack gets a mention of Hidden Power, often times with no given alternative.
On a non-breedable Pokemon it's especially bad, offering them as an example is unrealistic. Raikou could DEFINITELY use it, there's no argument there, but who's going to sit through 3,000+ resets? Having done a lot of reset-Mewtwo capturing I've seen how poor IVs can bite someone in the rear even with the supposedly ideal Nature. Nature and Type you might get with a lot of dedication, but it ignores the Hidden Power strength and IV totals. Both are critical if you're going to this much trouble to raise a Pokemon in the first place. A 30-50 strength Hidden Power won't be worth much.
EDITS: I figured a different approach to determine the odds of a favorable Pokemon would be to just look at each final characteristic individually and multiply their odds together, rather than trying to work the entire IV formula at once. Hopefully it'll be a little more accurate this way. I figured how Breeding factors in to IV odds in this approach and offered examples. Once again, Spoiler tag to conserve space:
[spoiler]Here's what I came up with:
Nature * HP Type * HP Power * Speed IV * Special Attack IV * AbilityNature = Add 1/25 for each acceptable Nature
If Everstone breeding, [25 + (1 per acceptable Nature)]/50
HP Type = Add 1/16 for each acceptable Type
HP Power = 1 for 30 (minimum) or above. 3/4 for 40 or above. 1/2 for 50 or above. 1/4 for 60 and above. 1/40 for 70 (maximum).
Speed IV & Special Attack IV = Chance of favorable IV. There are a total of 32 possible values (0-31), so take values that work divided by values that don't work. If you want to figure this the "quick and dirty" way, any value 21 and above is approximately 1/3.
If breeding, [(1 per parent with favorable IV)/4] + [(Chance of favorable IV when not breeding) / 2]
Ability = 1/2 if Pokemon has 2 Abilities and you want a specific one. 1 if you don't care or the Pokemon has only one Ability.
Multiply all fractions together (ignore 1's since multiplying by 1 does nothing) to get your odds of obtaining the Pokemon you want.
Examples:
Wild Pokemon, 1 stat gain w/ any of 3 stat losses (3 Natures), 1 HP Type, HP Power > 60, Speed and Special Attack IVs > 21, Ability irrelevant
= 3/25 * 1/16 * 1/4 * 1/3 * 1/3 * 1
= 3/14400
= 1/4800
Everstone breeding, parents have all favorable Speed/Special Attack IVs, 1 stat gain w/ any of 3 stat losses (3 Natures), 1 HP Type, HP Power > 60, Speed and Special Attack IVs > 21, Ability irrelevant
= 28/50 * 1/16 * 1/4 * {[2/4] + [(1/3)/2]} * {[2/4] + [(1/3)/2]} * 1
= 28/50 * 1/16 * 1/4 * {[3/6] + [1/6]} * {[3/6] + [1/6]} * 1
= 28/50 * 1/16 * 1/4 * 4/6 * 4/6 * 1
= 14/25 * 1/16 * 1/4 * 2/3 * 2/3 * 1
= 56/14400
~= 1/257
This formula reflects overall odds of each aspect individually, but there may be some room for error due to how a successful IV breed affects the Hidden Power formula, which can either hurt you or help you. Be weary of how IVs you are attempting to breed fit into the Hidden Power formulas. For instance, if you are trying to breed a strong Special Attack IV, but it's even and not odd, your Hidden Power Type value cannot be above 11, meaning you cannot have a Psychic, Ice, Dragon, or Dark Hidden Power if that IV is successfully passed to the new Pokemon.
This actually brings the Hidden Power Type odds down to 1/12 if you're looking for one outside of those four (and of course zero if you weren't). But that applies only on a successful breed to the Special Attack IV, which is 1/4 of the time for each parent. So, yeah, it can get very confusing.
Remember, at the end of the day, a bred Pokemon ALWAYS inherits 3 IVs from its parents. 1 from mom, 1 from dad, 1 at random. The other three are always generated from scratch. Which 3 are inherited and which 3 are from scratch are impossible to control, just gotta keep hatching until you get it.[/spoiler]