You don't need to put your heels down in downward dog, especially if it causes pain! It can take months or years to get to that level if you aren't flexible. I'm not flexible (really tight hammies and hip flexors) and I have never been able to get my heels down in that pose. I try to, but I don't force it because I know it will hurt! What's important in that pose is keeping a straight line from hands to tailbone, as well as from but to toes/feet.
straight legs are secondary to straight spine/tailbone up, as straightening the legs can cause the tailbone to tuck under, and work against you.
but it depends upon the individual. :)