If you put the white light from your (color) TV through a prism, you will get precisely 3 colors out - red, green, and blue. That's hardly all of them!

>otherwise it would be off white

This is false! For any given subjective white point, there is an infinite set of wavelength triplets which will achieve it exactly. The white from an RGB display is perfectly good, not "off white" at all.

> It's fair to assume that the whitish shade that eminates from a b&w TV is what is colloquially known as white.

Not a valid assumption! The "phosphor" in monochrome displays can take a wide range of subjective colors - very often it's blueish[0]...

> So I stand by my statement that a b&w TV contains all the colours.

...and can have all manner of emission spectra [1]. There's no telling what you'll get if you put that through a prism! That being said, the entries in that table for B&W TVs do cover most of the visible range, so in the absence of spectral plots, I may be forced to give you this one...

[0] https://www.avforums.com/attachments/s-l400-jpg.1057348/ [1] http://www.bunkerofdoom.com/tubes/crt/crt_phosphor_research....