That would a) let them off the hook ("How can we help him if he's lying/not telling us the whole truth?"), and b) put me in the wrong ("He's lying/not telling us the whole truth.")I think after all this pushback I would be inclined to simply stop telling them I use it 3 times a day. Not the way it should be, and a missed opportunity for them to learn something, but also not worth your energy.
Instead, I now have a secret weapon: Plank et al, 2005 !!
The most difficult part of this for me is that I have spent years believing that I should be able to make 2 injections last 24 hours (because that's what I've been told / that's what the official documentation says.) I have repeatedly watched my blood glucose creep up to 20 mmol/L, fully aware that I'm now poisoning myself, yet helpless because I've been repeatedly told that my levemir "is working" (cf. Martin Seligman's "Learned Helplessness").
Discovering "Plank et al." feels like a weight off my shoulders.