I have declined questions, and I have declined sitters because their energy didn't mesh with mine, and I knew it wasn't a good fit. It's always a hard call to make, and it doesn't happen often, but I think you gave that person the best advice you sensibly could have given them.
I didn't feel guilty, when I did that. My gut is my guide. I try to help wherever I can, but if it isn't the right fit, it would be like agreeing to date someone only because you felt sorry for them, or felt guilty about them. It would never work out well. Only answer honestly, and only answer what you can answer honestly, in my opinion. In the end, that is the best for all parties concerned.
And always obey your gut
ETA I guess you could have chatted with her, for free, and without cards, but that is a personal decision you need to make, and not based on cards (I agree that cards were not the tool for that question).