It is true that a 2560x1440 monitor is equivalent to 4 screens worth of 720p content. However it doesn't actually mean if you watch 720p movies/video that your video will take up 4 pixels worth of monitor space. I'll clarify.
When you watch 720p video and the monitor is in 720p mode (meaning you are running it in 1280x720 resolution), then, yes, correct, the actual pixels of each pixel in the 720p content will be equivalent to 4 'physical', native, pixels on the 1440p screen. It means that 1 pixel of 720p content in the source material is equal, physically, on-screen, to 2x2 native pixels worth of screen space on the 1440p screen. BUT keep in mind that is just how it converts if we are trying to think of it in relation to physical screen space. The pixel, even on the 2560x1440p monitor, is still just ONE pixel when we are running the monitor in 1280x720 resolution and watching a 720p source material. It's not treated as 4 pixels (2x2). And it doesn't require any scaling or stretching algorithm. The hardware takes care of doing that translation when you put the monitor into 1280x720 resolution but the aspect ratio is identical so there is no distortion or stretch at all. It's still truly just ONE pixel because your monitor is now in 1280x720 resolution. And it just means that the underlying hardware is converting 1 pixel of 720p source material to show up as 2x2 native 2560x1440 pixels. It will not distort the image at all. The aspect ratio is exactly the same (1.777...78). It's a perfect match.
There is no "upscaling" or "downscaling" happening. Upscaling and downscaling happen when you have source content that is higher or lower resolution than your monitor is capable of or if the aspect ratios are different. There are many scenarios. But the main thing here is nothing is being "upscaled" or "downscaled" if you view 720 on a 1440 (as long as your 1440 monitor is in 1280x720 resolution or capable of it).
Scaling of any type only occurs when you start getting into different aspect ratios or when you have source content that needs to be shown in a different target resolution. For example you have some older 480p source content but you want to view it on a newer 16:9 aspect ratio TV that's lowest resolution is 720p (just hypothetically). In this case there is going to be some scaling of the content. Also, yes, if you want that source image to "fill" the screen it will need to "stretch" some of the picture because 480p source material is a different aspect ratio (typically 3:2 versus the usual 16:9 or 16:10 we see today). Another example of scaling would be watching a YouTube video but you have your monitor set to native 2560x1440. The video plays in say 720p. But because your monitor is in a higher resolution than the content it is upscaled while it plays inside the player. I would still dare anyone to try to find differences between the upscaled version of 720p playing in an embedded YouTube video versus playing that same 720p video after switching your monitor down to 1280x720 versus watching that same video on a native 720p display (of exactly the same size, viewed from the same distance). The differences are truly minuscule.
If you have the same aspect ratios, same resolutions, or equipment capable of switching to that resolution, then no scaling or stretching of any significance will occur.
Anyone who thinks there is something wrong with watching 720p on a 1440p monitor and somehow the quality "changes" (it doesn't) doesn't know anything about aspect ratios and is also sitting too close to a monitor that was designed to be viewed with material at 4 times that resolution. Of course if you watch certain material in 1280x720 resolution on a 27" screen from 10" away at your computer desk you are going to see some grains (versus say watching Monday Night football in 720p on a 40" from 10ft away). But I can assure you there is no difference whatsoever, no distortion, scaling, stretching, etc... of any kind taking place. It's just simply that 1280x720 from that distance doesn't look so great when you compare it to full native resolution of 2560x1440 (obviously - that's 4 times the pixel density).