Most myths had a reason behind why it came in to being. with this one that you brought up I’ve wondered what could’ve motivated it. Here are a few reasons I came up with:
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TVs picture quality is a LOT better than it was 30-40 yrs ago. With flat panels the strain on the eyes has been reduced quite a bit.
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Sitting too close to the TV may not be bad directly, but if you think about it the eyes do use a lot more muscles to look at things up close. Ofcourse the kids are better at it but that may tire out eyes over extended periods (may even cause headaches). Plus if you are that close then you don’t see anything else besides the TV, peripheral vision or otherwise. Sitting far away you tend to look at other things (get distracted) which is prob a good thing, i.e giving the eye muscles to relax as you look away at things further and different (screen saver syndrome)
Over all there is a corelation for between people who read a lot with eyes problems early on in life, so I think that has to do with #2.