This is mostly true. With a small TV (36" and less), the lines of pixels are put so close together that from regular viewing distance you wouldn't be able to tell the difference in definition/quality between 1080p and 720p, even a video expert would have a hard time distinguishing them.
It's like if you took a poor quality image of a large size on the web and shrunk it down to a very small thumbnail size. All of a sudden, the picture quality of the thumbnail looks very good, yet there is no more definition/detail in the thumbnail than there is in the original image. It's just that the size of the picture has been reduced so there is effectively an increased amount of definition/resolution relative to the size of the image.
So with a smaller TV screen, there is more picture definition per square inch of display than there would be on a larger TV screen so that 720p video can appear to have very high definition making it hard to distinguish it with 1080p. Basically on a relative scale, it's much easier to see the difference on a very large screen (e.g. 100") compared to a very small screen.
This is the case for video games, blu-rays etc. Whether the TV supports 720p or 1080p and whether the video output is 720p or 1080p doesn't really matter on a small display.