In a case, however, where executing something specific cannot work, you have an implicit contradiction wherein a direct explicit[/] contradiction does not need to occur.
An example of this would be Commander's Strike. It has an attack roll of 'Your opponent makes a basic attack' and a hit component of 'the attack does +4 damage'. As most powers are templated that is nonsense, 'as your opponent makes a basic attack' cannot possibly hit as it is not an attack roll.
However, game elements must always work, and therefore SvG forces it to work by having it plow through game rules that say it simply cannot. Nothing contained within it can say it does not work, it works because it says it works.
In the case of Polearm Gamble, yes, actually, it works because it says it works. That's good enough to satisfy SvG, and if more general rules say it cannot possibly work, then those rules get trumped.
The rules cannot make specific elements simply not work, not so easily as that. That is not a logical possibility in 4th edition. Specific Vs General is a guarantee that they do. If SvG can't make Polearm Gamble work, you're not using enough SvG.
The difference between this, and using a non-ranged weapon, is that once you accept that a situation exists where Polearm Gamble can work so long as you use a reach weapon, it now works, SvG is satisfied enough, and the rest of the rules of the game operate as needed. The contradiction is resolved.
To sum up:
If a game element simply cannot work, the rules are wrong. Specific vs General makes sure this happens.
If a game element can work, but in this specific case doesn't work because of a specific scenario, Specific vs General makes sure the specific case trumps the game element, as it is now the general.
The moment you say 'You can never use Polearm Gamble because the rules don't allow it' you've identified a contradiction and ergo, MUST apply SvG until that contradiction is resolved. There is no such thing as 'it cannot work' in 4e.