HP8710 won't print greyscale without cyan cartridge

[Old Engineer]

Hi, any advice will be welcomed ....
The yellow cartridge supplied with my Officejet Pro8710 ran out. I got a screen message to say the ink was low and an option to print greyscale only. That was great and kept me going while I ordered a new yellow cartridge.
I just fitted the (genuine HP) yellow cartridge and immediately got a message saying the cyan cartridge was empty and I cannot print at all until it is replaced. So I was actually better off before I fitted the new cartridge.
I don't understand why I can't do greyscale until I get a new cyan?
Or indeed how the cyan became empty when I clearly haven't used it since the yellow ran out.
John

 

[Old Engineer]

Next stage from the above ...
Before fitting the new cyan cartridge I checked the ink level panel and magenta was at about 1/4, definitely not showing low or empty. You may guess what happened next, as soon as I put the cyan in the printer refused to print because it said the magenta ink was empty.
Is this just a scam to sell replacement inks in threes or have I missed something?
BTW, I'd ordered a magenta because I guessed what was going to happen, at least the printer did not suddenly discover the black was empty when I fitted the magenta