The only hole in that theory is that Bella didn't go to B&R and, as a Royce, Jill's sister likely went to B&R just as Jill is doing now. So unless Jill's sister went against her family's wishes and went to the same college as Bella, it might not have been during their college days that they knew each other.
Remember that Bella is 13/14 years older than Jill which means there was a potentially similar age gap between her and her sister if she and Bella were around the same age. In the Polaroid picture, Jill looks like she could be about 10/11 making her sister and Bella around 23-25 at that time and maybe this is around the time when they met; after they graduated from their respective colleges and ended up working somewhere together. They might have known each other for a couple of years before the sister's death and Bella grew close to Jill hence why she's been like a surrogate sister to her since then.