I used to be a scanner operator and from the printing industry, you guys are mostly right but not completely.
True the DPI is related to image resolution, and 300 dots (or pixels) per inch is required to create a good halftone dot for printing. But when you resize the image, you can make matters worse.
Take an example: a 3 X 5 image at 300 pixels wide.
If this image is 72 DPI, that means 72 pixels for each inch, which makes it 4.16 inches wide.
BUT
If you resize this image to 300 DPI, so there are 300 dots in each inch, and do not resample the data, you now have 300 dots in each inch and the image is only one inch wide. (300 px wide, 'member?)
But the FILE SIZE is exactly the same.
If you were to resize this very same image, and resample the data, this will give you an image 4.16 inches wide and 300 DPI, and it will also increase the file size, but there's a catch: You go from 72 per inch to 300, where do the extra pixels come from?
This is called interpolation and is very similar to the algebraic description, a mathematical guess at what goes between.
In your original 72 DPI image, you have two pixels right next to each other and you want to now fit in and extra 228 pixels in that space. So the graphic program does some estimating of what's on ether side of the pixel to figure out what goes between. The bottom line is since there's nothing there, the best you get is a guess - a really large file size but still the same choppy image.
So if you RESIZE your image with the intent of getting the highest rez possible, you need to make sure that resample image size is turned off, then check the INCH measurement to make sure it's what you need.
In my 300 pixel wide example - the best you'll get is a 1" wide image. In Rolex's 1792 x 1200 pixel example - this gives you a 5.97" X 4" image at 300 DPI.
The reason your file size got so large is you resampled the data at the current print size. You need to turn off image resampling and it will be hunky-dory.