I don't think this is possible.
720P means a progressive HDTV signal format with 720 horizontal lines and an aspect ratio (AR) of 16:9 (1.78:1)
1080p is a set of HDTV high-definition video modes that are characterized by 1080 horizontal lines of vertical resolution and progressive scan, meaning the image is not interlaced as is the case with the 1080i display standard.
The resolution of them is different, and when you convert the 1080p video to 720p video, I think the ratio also changed.
yes it is possible, any 'quality loss' if done right will not be visible for consumer use, if it were for commercial use then it does matter, however they will have had the funding for a 'proper' video editing set up.
You can do that without "losing quality". the 720p files that i have are not that much worse quality than the 1080p. If you manually shrink the video player of a 1080p file and put it next to a 720p video most people would not be able to pick out the 720p. But technically it would be lower res and lower quality. But to save space you could reduce them down to 720p and use a good compression codec, like xvid or x264.
But as we move to larger resolutions the differences in resolution should become more apparent.