If your gp has advised that testing is not necessary then they could include something like that in the letter hopefully. It will stop work flapping. Although of course you can test if you want too - most of us do.
It sounds like they've just seen the word diabetic and gone 'Ape'! If a letter from your GP is what they require for the file!! then let then have it, but i'd make sure the GP in not one that will charge you for such a letter as some would. If there is a charge then tell your employer to write to them for this and let them pay for it.