There's no physical size to an image. The size that it prints out would be dependent on the resolution and your printer.
That's not true.
The physical size of the image is a function of the DPI setting (number of pixels/inch) and the number of pixels on the X and Y dimensions.
Modern file formats such as PNG and TIFF have a DPI attribute which can be set using image processing software such as The Gimp. For example, if I have a 100x100 pixel image with a resolution of 100DPI, it should be 1" square when printed at the correct resolution, if the resolution is then set to 50DPI it will be twice the size but it will look worse.
For some reason Eagle isn't scaling the image correctly so a 2.6" board is being skewed to 2.62" by 2.61", although this won't be a problem 99% of the time, there's always going to be that 1% of the time when it is.
Attached is a screen shot of my PCB in the Gimp showing the scale function, after I've scaled it to the correct size. Notice the pixels/inch setting is 300, the image size is 2.6" by 2.6" and the image is 780x780 (see title bar)? It's no coincidence that 780/300 = 2.6
The resolution of the printer is just the maximum resolution it can do and is not necessarily the resolution everything is printed at and the same is true for a scanner. The only problem with putting PNG images on the website is that some crappy imaging software ignores the resolution and tends to print at the screen resolution so I suggest that the user to import the file into a MS Word or OpenOffice, which honour the resolution setting and print form there. I don't know about web browsers, I suspect it varies but wouldn't be surprised if the screen resolution is used most of the time. I've also considered using SVG (Inkscape can convert PDF to SVG) but still isn't widely supported.
Not certain why you are exporting to a image. Print it directly and it's perfect. I haven't used it, but you can print to PDF or PostScript as well if you really need to take it somewhere.
I export to a PNG to upload to a website. I could use PDF but Adobe has a nasty habit of scaling to fit the paper
Feel free to switch to Kicad or gEDA. The former is younger, but easier to use and with Windows binaries, it appears to develop quite fast. The latter is older (more features), but is not very easy to use, and doesn't distribute Windows binaries. Both are open source and have transparent (plain text) file formats.
I will certainly Kicad and will no doubt use it for most of my projects but I need to leard the proprietary software used by most companies too.