People on insulin pumps can essentially eat what they want, whenever they want. Of course they have to eat within reason so they're not taking 100 units of insulin. Your patient is very used to this and having to eat when you tell him/her is probably very frustrating to him/her. Telling him/her to "lay off the sugar" is not helping. You aren't only covering conventional sugar. You are covering all carbs, so him eating a banana would still require insulin.
Pumps use Novolog, Humalog, or Apidra (short-acting insulin) and pens come in those as well as the long-acting insulins. If you are covering his/her food intake then you are using a short-acting insulin, probably the same one he/she uses in his pump. There is no difference between the two (pump insulin vs pen.) The pump is just easier, no shots. If he/she doesn't mind sticking him/herself every time he/she wants to eat and you have the time to be in there then I believe you should allow this. He/she could probably so his/her own shots as well, no reason to be doing it for the patient when they are fully capable. I am for patients being able to keep with their home schedule as much as possible, within reason.
If he/she is eating poorly this could be a good time for education. Could the nutritionist speak with the patient about healthy choices? Even if he/she doesn't listen they have the information and will hopefully use it at some point.
If the patient feels as though you will say no to his/her request to eat they may be just doing it, no coverage which could account for some of their high blood sugars.
Good luck. Type I Diabetes is a tricky disease to manage. Each body is so specific, it is hard to know what is right for THAT person. Just a question, is this inpatient?