From JWST Observatory Characteristics/JWST Orbit https://jwst-docs.stsci.edu/jwst-observatory-characteristics/jwst-orbit
Because JWST is solar powered, it cannot pass through the Earth's shadow during the mission. Orbits are selected that avoid shadow crossings, by selecting the launch time for a given launch day.
This diagram of the orbit indicates the only portion of the trajectory which risks an eclipse is the portion of the insertion which is radial to the Earth’s orbit. Once JWST is in halo orbit, the whole eclipse shadow thing is a non-issue.
I suspect the "no eclipse permitted" is a vestigial statement, put in early documentation and perpetuated ever since. Since it is a complete non-issue once the telescope is in halo orbit, no one has ever edited or qualified the statement.