When you are working in the computer and looking at pictures thru your monitor the dpi is unexistant. The dpi only comes into play when you want to print something. In other words, printers understand dpi but monitors don't.
What does matter for your monitor is the resolution. That is, the number of pixels horizontaly times the number or pixels vertically (i.e. 800x600). The picture that you attached is 393x392 pixels. It does say it is 72 dpi, but all that means is that a printer will print that at 13 x 13 cm. (if you were to increase the dpi mantaining the priting size you would need to icnrease the resolution).
So Maya will import pictures at any dpi, because Maya simply won't care about that, it'll only look at the resolution. (actually I think it does read the dpi for something else... but that doesn't matter right now).
If you want to render a picture that will print at 300 dpi at a certain size (let's just say 10x10 cm), then just go to photoshop and chose new. Then under resolution type 300 pixels/inch. Then Change the units of width and height to "cm" and for the values type 10 and 10. Then you hit Ok (or create or whatever it is). Now click "Image>Image Size...". Here you can see what resolution you have to render from maya to get a picture that size (if you want to print it, of course). So in this case it would be 1181 x 1181 pixels. So now you go to maya, change the render resolution to 1181 x 1181. After rendering open the image in photoshop and change the dpi to 300 and make sure the dimentions are still 10 x 10 cm and that should do it. I think... :p or something like that anyway.
There can not be Good without Evil, so then it must be good to be Evil sometimes.