Not "true".
CRT's don't work like modern "pixel mapped" screens, they're a electron gun blasting RGB onto a shadow mask. Hence why you certainly had CRT PC monitors and they could support multiple resolutions, which one was native? real answer is all of them, also notice the higher resolution one was often unreadable and tiring; which means the panel had extinguished it's capability to solve detail at that setting.
All this to say, "upscaling", the process of taking a 640x480 image, processing it via internal chips and creating a higher resolution fucked up composite of it... Didn't take place on most HD-CRT-TV's.
There was simply no need for it, technology wise.
Thing is, said games had jaggies and big pixels, it's only normal that a panel that could resolve so much detail could evidence that fact, but it's not "upscaling", it didn't involve extra processing or results ranging from softened detail or badly de-interlaced 240p, heck, it shouldn't deinterlace 480i either (most if not all HDTV's internally do so). They're certainly not supposed to [lag].
I understand the natural differences between CRT and LCD and that CRT displays don't have a "native" resolution, and that there shouldn't be a reason for a CRT display to upscale, but this doesn't change the fact that the CRT HDTVs I've tried lag and don't even flinch when you display a high definition television OSD on top of a low-resolution SNES image (which would suggest upscaling and de-interlacing). I couldn't tell you why, but I would put down money that they were doing additional processing on the image.