Well, 4e doesn't really spell all this out in any detail. While rituals don't have keywords associating them to power sources, they DO seem to be associated with specific skills which usually identify them with a power source in a loose way. I mean, MOST rituals you could say "yeah, that's a Primal/Arcane/Divine ritual" and there are clearly power-source-associated ritual components as well.
I agree.
Whether they are typed magic or untyped magic I don't think really matters one way or the other here though. They are magic that require specific prerequisites and not everybody can do.
But beyond that... what would be the problem with applying page 42 (improvised actions) to carrying out activities that are essentially rituals?
4e DMG page 42 for "actions the rules don't cover" is sort of begging the question here.
Page 42: "Cast the Action as a Check: If a character tries an action that might fail, use a check to resolve it."
The instruction that if you think it is possible but they might fail use a check does not tell us to use a check for something that cannot happen.
Whether people can carry out activities that are essentially ritual magic without meeting the requirements of ritual magic (ritual caster feat or expending one shot ritual scroll and specific level, check, and component requirements of the ritual) is more a world question about magic in the world and how a PC can access it.
Wouldn't the people in a campaign world call those 'rituals'?
If they worked and looked like rituals that did magic, sure, observing characters in the world would likely think of them as ritual magic.
For instance, in my game once a Wizard wanted to poison a bunch of Jermlaine who infested the air ducts of an ancient dwarven city. So, she undertook a Skill Challenge in which she used Arcane ritual components to cast her Stinking Cloud daily in such a way that it filled the ducts with a poisonous fog which killed most of the Jermlaine. I'm entirely certain the other characters called it a 'ritual'. I agree that it was mechanically handled as an SC, but I think that's just a reflection of the fact that carrying it out, without a formula, was unusually difficult. While it never came up I would have probably let the character experiment with the technique for a while and produced a standardized ritual formula for it.
So, certainly if we are discussing 4e, questions of what is and isn't magic vs mundane or if something is a ritual or 'something else' are really pretty gamist. Narratively its all 'doing magicky stuff'.
I wouldn't say everything in 4e is doing magicky stuff. The 4e arcana skill can explicitly be used to manipulate magic. Other skills do not explicitly say they can be used to manipulate magic on their own.
A prayer that does magical effects is doing magicky stuff. If a prayer on its own can not do magical effects it is not doing magicky stuff, it is just a prayer.
5e has a different baseline for magic. 5e arcana skill does not explicitly allow you to manipulate magic.
3e knowledge arcana and spellcraft skills did not explicitly allow magical effects on their own.
AD&D had a few divine intervention mechanics and narrative elements spelled out. Some settings had specific supernatural rules anyone can tap as well (Ravenloft with curses and dark powers checks).
I don't recall any relevant examples from Basic.