Here are two mondo-sized pixels, one orange, one red:
Pixels represent the file's data. They have no specific size or dimension, they are just bundles of numbers that represent information. Pixels have no dimension that can be measured in terms of "per inch" until they are represented in the physical world.
Representing this data in the physical world is tricky. Our monitors and printers don't have access to every color you have in the original scene. So in most cases, they are represented through dots. Dots are little blobs of color (ink or pigment) that when viewed at a distance merge together to form color:
So as you can see, the definition of the pixel kind of goes away, but at a normal viewing distance it's kind of hard to tell that the pixels represent orange and red. Fair enough. Make the dots smaller:
Well, that's better, but now the pixels are distinct again, and the image will appear all pixely.
What does this mean in the real world, a printer screen with a lower frequency can have a lower ppi without resolving individual pixels:

(click for detail)
However, a higher quality printer with higher screen frequency will require more pixels per inch (ppi) in order to avoid pixely results:

(click for details, flower image courtesy of Eric Gunther
File:Bidens flwr.jpg - Wikipedia, the free encyclopedia)
So no, you're not going to get away with lower ppi on a better printer. But photoprinters require as continuous tone as possible, and have outlandish screen frequencies. So for photography, the best solution is to ensure that the pixels are smaller than what we can see, this is why 300ppi is kind of teh standard. Beyond that, you're not going to get much better results, because the eye cannot resolve below about 1/300"