Does that make the DPI irrelevant? No.
DPI comes into play when we take our images and place them into a page layout program, like Adobe InDesign. In the page layout program the file that is marked as 72 dpi will come in at a very large size (25" x 16.7") and will look pixelated. The file that is marked as 300 dpi will come in small (4" x 6") and be of a finer quality. Here is an illustration of how they would look when placed into a standard 8.5x11 landscape page in InDesign:
The sad part about all this is that many people will find the quality of the 72dpi image acceptable enough to print. That is why setting your image files to 72 dpi on its own is not enough to deter their being swiped from the web. They also need to downsampled to a smaller pixel dimension. For places like Facebook and Flickr I usually downsize to around 600 pixels on the long side, and also add in a watermark.
Even that is not really enough. Here is the same 8.5x11 page in InDesign, but this time the image files are 600x400 pixels (but still 72 and 300 dpi). Again, the red line shows the 8.5x11 page, the yellow line is around the 72 dpi version and the green line indicates th 300 dpi version:
As you can see, even here these 600 pixel wide images are still printable at an acceptable quality for many people. If you printed out of Photoshop without changing anything in the files you would see a similar situation. The 600 pixel wide image at 300 dpi will print at 2 inches wide, while the version marked as 72 dpi will print at 8.3 inches wide.
Based on the above, my personal advice on setting resolution is to set your DPI HIGHER rather than lower if you want to want to make it more difficult for your images to be "borrowed" and printed. If the person borrowing the image doesn't know what they are doing, the higher DPI image will print smaller (at better quality). The lower DPI image will print larger; probably at a quality good enough for the person using your image.
Of course, if the image is just being borrowed to be used on a web site there is little you can do to prevent that other than not share any of your images. If the image can appear on someone else's screen, they can take it. Best advice I can give here is to develop a recognizable style and a watermark (even though that can be cloned cropped out).
To reiterate again, the important numbers when distributing your files are the pixel dimensions, NOT the DPI setting. Keep the dimensions small for proofs, Facebook, Flickr, etc. And find out exactly what your clients need if they are going to be printing your images.