You are not reading the manual correctly I'm afraid. I don't want to be pedantic

but this will be found on searches and is, I'm sorry, wrong.
On page 86 a table clearly shows Matrix metering is Compatible with Ai and Ai-S lenses, the limitation is with lenses modified to Ai by the Nikon or other kit. This is because original AI / Ai-S lenses have lugs built into the back of them to give the meter extra information. These lugs were not added with Nikon's AI conversion and are necessary for the matrix metering of the F4 or FA.
The table appears in the F4/ F4s Manual referenced as
Printed in Japan 9&141-804 (S155)
Are you getting confused with the Programmed Auto Exposure Modes (PH, P) these require a CPU enabled lens and if selected without such a lens will show A (Aperture Priority) and turn off matrix metering, showing CW enabled, in that mode?
I cannot see anywhere in the manual which states, as you say, a switch to CW just by mounting an AI/AIs lens, if I am wrong please quote the entry.