My answer is: try downward dog both ways, see how it feels for you. For some elements of yoga alignment I’m as fastidious as they come. Ask my students; they’ll tell you just how boring I am about where the front knee is in Warrior 2.
Elaine comes to my Thursday evening class and often mentions her tight hamstrings. I could see her last week looking uncomfortable in downward dog. Clearly straightening her legs and trying to get her heels back onto the mat. Somehow I could see the stress of this travelling all the way up the back of her body and limiting the movement in her shoulders.
I told her it was okay to bend her knees and not to worry about the perfect idea of downward dog with the legs straight and the heels on the mat as most of us don’t achieve this and it can be an unrealistic goal for many. As soon as the knees are bent, the hamstrings are released and so they can then often lengthen at their other end; where they attach to the pelvis. This can reduce strain in in the lower back, in short, making downward dog feel better and easier.
Hesitant at first, as she had been told by another teacher to have straight legs, Elaine tried it. Obviously different teachers have different cues and different beliefs about poses, so I advised her to try it both ways and take whichever felt more accessible for her, her shoulders more able to open, her lower back more released.
I’m not a huge fan of the yoga-pose-shoulds, instead into what feels good and right for each individual person. There’s nothing wrong with having a picture of where to aim in a particular pose, but to hold oneself in an uncomfortable version of a pose because it’s believed to be more accurate is a mistake in my opinion. Keep an open mind, take the adjustment, try a version of a pose that you never have before. You will often be pleasantly surprised.