So "If a summoning power allows the summoned creature to attack" -- you are imputing "by making the creature exist, the summoning power is what allows the summoned creature to make a basic attack"?

Because if the basic attack isn't what allows the summoned creature to attack, then using the summoners game statistics is wrong. (From what I can tell, no rule actually describes what stats to use in that case) You could impute that you should use the summoner's strength because the summoned creature uses the summoner's strength if they try to lift something, but the rules *don't* say that the summoned creature actually has that strength (it jumps through hoops *not* to say that), just that the summoner's strength should be used in (1) ability checks, (2) attacks that are allowed by the summoning spell.

I'm also confused by "Summon Shadow Serpent" note. They explicitly state that the Summon Shadow Serpent does not have an attack allowed by the summoning spell, and the summon has no attack power, and state that this is part of the "Summon Shadow Serpent" power (not a rule added here). Doesn't that sort of throw out your entire chain of reasoning pretty explicitly? I don't see anything special in "Summon Shadow Serpent" that blocks using a basic attack using your logic, which implies that it has a basic attack power, which is an attack power; the rules text meanwhile states that the correct conclusion is "it doesn't have an attack power", which means your chain of logic cannot be correct for "Summon Shadow Serpent".