I've used both DMS ankle boots + puttees and IDF boots. The IDF boots were better.
Even better was the IDF method of not shining your boots - slapping on polish was enough....
With the ankle height boots though I found puttees were quite a good idea (in the UK climate). They supported/protected the ankle and sealed the tops of the boots from dirt. Too much hassle to take on and off though.
It looks like some journo didn't check their facts. I was in IDF airborne from January 1981 - never heard any reason given for the red boots other than it was for the airborne division's own esprit de corps.
The red beret - well that's another matter altogether.