To me it sounds like she's made a choice somewhere along the way to lock her emotions away. Since it sounds like she was the caretaker, she may have had to out of necessity as taking care of someone you care about for a while, and seeing them in pain, is highly stressful. It was a choice for emotional survival in order to stay focused on caring for the parent. She probably feels relief now, and on some level feels guilty that she feels relief when others around her are feeling the pain of grief. That's probably why she keeps apologizing.
If this is the case, her attitude isn't bizarre or meant to be hurtful - she's simply still in an emotional survival mode. Talking about the death academically helps her detach from the emotion of the loss and keep the emotions locked away. The pain could be so unbearable that she may fear she'll explode, so it's simply easier to keep them locked up. However, the pain of grief will eventually become too much to hold in, and she'll eventually need to allow herself to feel through the grief. Something, someday will trigger that release.
I was not a care taker for my mother when she suffered with cancer for a 3 year battle, but for other reasons in my childhood, I had decided to "turn off" my emotions. I showed happiness and I showed anger - but not much else. When my mom passed, there was a sense of relief, like our family had been holding its breath for 3 years, and now we could finally relax. I was the oldest of the kids, and was always the "responsible" one. I didn't cry much at the funeral because I felt the need to "stay strong" for my dad and brother and sisters. Instead, like the rest of my emotions, I bottled up my grief. Then a couple days after the funeral, I had to go back to college where there was no room to grieve as I had to stay focused on my studies as best as I could.
It took 5 years before I was in a place to allow myself to finally grieve the loss of my mom. I was on about an 8 month roller coaster of emotions as I allowed myself to let all that suppressed emotion out - and it physically hurt as I was still instinctively fighting to hold it in but at that point there was just too much and I couldn't hold it back any more. After finally getting through it, I knew I had finally fully grieved and was fine every since.
So, is it strange that she hasn't yet grieved for a parent that died 2 years ago because she was focused on staying strong to care for another who just recently died? Not in the least in my eyes. It could very well be several more years before she'll be able to allow her guard to break down to the point where she can grieve, and when she does, it won't be pretty. Not only because it will be hard for her to let the emotion out while her instincts are probably to keep the held back, but also when she finally does grieve, she won't have a support group grieving with her as everyone else is grieving now - she'll be grieving alone in the future.
With that in mind, if you stay in contact with this person, and several years from now she starts acting "strange", it could be she's starting to let the grief out. If you suspect or learn this is the case, be a good friend and be there to support her.
That's my 2 cents on the topic.