No, even if you have some of your own insulin left, if you don't have enough to meet your needs, you need to use exogenous insulin. And the pump is just another way of delivering it.
Type 2's are generally less prone to hypos, because they still have functioning alpha cells to secrete glucagon. That doesn't mean they can't go low (anyone can go low in the presence of too much insulin!), but it's not as much a problem as for Type 1's who have lost alpha cell production.
People are negative because there is a link (note it's not a proven cause, simply a link) between obesity and T2 (roughly 60% of T2 are obese/overweight). So they view T2s (actually all) diabetics as having caused their disease. Can being overweight cause insulin resistance? Yes. Does that mean it is always the cause? NO! Look at it like smoking. Does smoking (being overweight) increase your chances of lung cancer (diabetes)? Yes. If you don't smoke (be overweight) are you safe from lung cancer (diabetes)? No. I'm T1, 5'11" and weigh a shade less than 150. I run and do weights on alternating days and am in great shape. I get told nearly daily I caused my diabetes. When I point out I'm not overweight then it becomes: too much sugar, too much soda, too much beer, too much alcohol, too much partying, not enough veggies, too much meat, need to become vegetarian, etc. No one in my family has diabetes of any type. It's also worth pointing out that some (not all, and I've heard no statistics simply anecdotal evidence) T2s can control through diet. But not all, as many will slip down and down even with proper diet and exercise and eventually need insulin (BTW, diet and exercise was the prescribed treatment prior to the 20s when insulin therapy came about and life expectancy was four years after diagnosis if you were lucky).
Anyway, I'm not trying to attack or be negative toward you, your daughter or any others. Just pointing out what I've seen, heard and read. I for one think that most of the negativity comes from a lack of education from PWOD and from stereotypes the general public holds towards diabetics.