Is there a way to get Illustrator to know how many pixels are in an inch?

Question

Hi, this is my very first post so please be gentle!
I've scoured these forums and found no solution to this problem.
I'm using Illustrator CS5 to make graphics for print. I need to print said graphics at 300 DPI, but this seems impossible.
Illustrator has plenty of settings that tell you it's at 300 DPI, but it never ever is.
Here's the new file dialog:
In this example, I'm making an image that I want to print on a letter sized piece of paper. The example is square, but that's not important. 8.5 inches at 300 DPI is 2550 pixels. Watch what happens when I change the unit to pixels:
Despite the raster effects set to 300 PPI at the bottom, it thinks that 8.5 inches is 612 pixels, which is 72 DPI, NOT 300. Watch what happens when I choose the correct pixel resolution then switch it back to inches:
It actually thinks I want to print a 35 inch poster with horrible gif resolution.
You might say that the pixels are the only thing that matters when it comes to print, and you'd be correct, if I didn't want to print via a PDF. When I save a drawing like this at the correct pixel resolution to PDF, then try to print it at the actual size (300 dots to an inch), I get something like this because Acrobat thinks I have a 35 inch high document:
Well, you might say, why don't you just print it to fit and you'll be fine? Sure, I can tell my print dialog to fit it to the page, but it doesn't fit it to the actual page size, it fits it to the printable area, which is maybe an 1/8th of an inch smaller on every side of the page, which means my 300 dots will never fill an inch exactly on my printer. I could never in a million years print a usable ruler.
Before you ask, yes the Document Raster Effects Settings are also 300 PPI and it has no effect.
Does anyone know what I'm doing wrong?

Answer 1

Coming late, and maybe it's covered, but I noticed this earlier quote: ""I use Save As, then choose PDF from the dropdown menu. The actual size of the PDF will be 72 PPI. I can try printing to PDF, and see if it makes the same giant PDF..."
I think you may be getting hung up on resolution when there isn't one. PDF files DO NOT HAVE A RESOLUTION. Like Illustrator files, they are a vector format.
A PDF file might contain no images at all, then it is impossible to talk of resolution at all. Or it might contain images, but these might all be different resolutions. Sometimes, it so happens that all the images have the same resolution, then it is just about possible (but not necessarily useful) to talk about resolution. A number of utilities claim to report the resolution of a PDF but just make it up! Where did you get the 72 dpi figure?
Another common error is to think of "100% scale" as being a universal thing, and expecting something viewed at 100% to be the same size in all apps, so to think something is wrong when they are not. This is simply an error: each app has its own different idea of what 100% means and you cannot compare apps this way.
If you want to know the size of a PDF, first realise each page COULD BE a different size, though they usually aren't. Open in Acrobat and hover the mouse in the bottom left corner until the size appears. This is in inches/mm; remember there cannot be a size in pixels.