I squirt often and for me, it matters not whether I am raised or not. I squirt in doggy/standing/oral......for me it just depends on how turned on I am and manipulation of my g-spot. When Mrs. H has squirted before, have you raised her? Or was it that she happened to feel more fired up for some reason.
It depends on each person really, I can squirt in different positions, mainly when my legs are pushed down onto my chest (flexibility is a godsend but sadly not a natural talent) like knees touching boobs or when i'm on top. I think it's mainly down to how aroused you are and can be an 'in the moment' thing.
Play about with different positions and see what works for you both, it'll be fun experimenting and you can have a giggle with odd positions ^_^
I only squirt during certain times in my hormonal cycle, so your partner could be the same. Me being on top is always a winner for orgasms and squirting, or having someone who's talented at internal fingering can make me squirt, but I expect everyone is different in what works best for them, the fun part is experimenting and finding out :)
Try the pillow thing then ask your partner for feedback I reackon