Knowledge can make one's position/argument stronger.

It kind of sounds like the OPs sister won't take a simple no. Otherwise this post wasn't even needed.
I only suggested a possible solution as the relationship with her sister is important to her, and she didn't want to feel guilty.

Sadly, sometimes a simple no can cost you (or damage) a relationship. When that no comes with an explanation the sister can relate to, hard feelings can be greatly lessened.