In PAL & NTSC the colour carrier was a multiple of the line rate.

Not quite.

In PAL, the subcarrier is 4.433618 MHz and the line rate is 15625 Hz,
the ratio is 283.75512, not an exact multiple.

When I studied the thing in the 60's, the explanation was to find
a frequency at as non-integer rate as possible, to get rid of moire
effects.

This is not a correct explanation -- and I'm certain your numbers are wrong
(you've rounded off the line rate).

The subcarrier HAS to be a multiple of the line rate -- specifically, an odd
multiple of half the line rate -- or the sidebands of the color signal will
not properly interleave with the sidebands of the luminance signal.

By the way, moire is not capitalized. It is not a person's name.