Hi Renee and sorry about your mother's disease!
I'm not sure of the rules, but I suppose it depends how a person feels at the time of diagnoses? I was diagnosed with 378 and felt just fine. In fact the doctor didn't find out this till a few days later, when test results came in. And her assistant called me and asked to come over, but I said, why, I have an appointment tomorrow? Meanhwile I went to some fancy dinner at my nephew's and ate lots of everything I was not supposed to (and I didn't know that yet) and was still feeling OK. Now I strongly suspect that after that dinner I probably was at 500 too.
And you are right - 240 BG is too high, but it's going down and it's expected to be in higher numbers for a while, they can't just go to the normal in a few days - it takes weeks and months sometimes. And be prepared that your mom feels worse than she felt before for a while too. The thing is that body gets used to the high numbers and when they go down and especially when they go down rapidly - you can expect some unpleasanties as body has to ajust again.
Does your mom has a meter? The best way is to start testing her BG and take the matter in her own hands as knowing what she can or can't eat safely. Diabetes is no fun, but can be managed and your mom still can have good life.
Good luck and hugs to you and your mom!