There is a lot of truth in the statements that are against you shooting the eclipse, but some level of exaggeration too.
I've never shot an eclipse, but I shot the Venus transit in June 2012, at around 6:30pm. I was using a 70-200 at 200 and I didn't have an astronomy filter, I only had a polarizer and an ND4 which I stacked and then used f/32 and 1/8000sec. Nothing burned, nothing got damaged, but the pictures were too bright, so you can't see Venus in front of the sun (interestingly, you can see it in the ghosting). That's attached picture number one.
Then I've taken the second picture, much closer to sunset, also at 200mm with no filters whatsoever, at f/4.0 and 1/4000sec. This one was followed by another bunch of pretty much the same shot, trying to get the seagulls at a nice angle wrt the sun. Nothing burned up this time either.
The flaw in the analogy with the magnifying lens is the size of the dot. If you get the "dot" to be 35mm, it won't be all that hot.
Use common sense. If you point a super-tele at the sun at noon or something, then there is a very good chance that your equipment will get damaged, if you use a 200mm or less you'll probably be fine (but don't send me the bill if things break
).
I will +1 the opinion that the eclipse is a cliche that is not even worth shooting though, unless maybe if you have something longer than 1000mm, in which case I'd put a welding glass in front of it!