Take this picture for example.  Would a model release be necessary for a picture like this?

The dog is mine and the person holding her is my son. 

The dog is mine and the person holding her is my son.

So it would be easy for you to submit the model release for your son. That way you don�t have to worry. Personally, I would say you don�t need one, but yes, depends on the agency, and some agencies would say that someone could recognize themselves from the clothes. Silly, but... Bottom line, their game, their rules.

Wow, this is really a foggy issue.  I would think that as long as a person can not be identified, a release would not be needed.  I kind of think about it like a court case.  Could this picture be used to positively identify a person in a court case?  I don't see how.  The person could claim it was them, but there is no personally identifiable items in the photo. 
But I am just saying my thoughts on it.  Apparently,  there are no hard fast rules on this.  Take this photo for example.  I cropped out everything but a hand.  How could any be identified by a hand?

There is no law on this in the US (and each country is different); it's just risk avoidance on the part of the agencies that sets their policies. They don't want to be sued - even if you win, that eats up profits. The agencies have no interest in establishing clear legal boundaries, just in staying far enough inside they avoid lawsuits.

As a photographer, you probably want to be risk averse too - royalties are small and lawyers are expensive.

So, you follow agency rules even when you don't agree with them or think they're being nervous nellies. At one time (years back) Dreamstime rejected images you provided a model release for if they didn't think one was needed - only part of a face, or hand and arm was showing! As you were penalized for rejections back then, it was a truly silly policy, but they'd just introduced searching by model release and they thought this would mess their search up.

Context, clothes, hairstyles, hardware (like a cane or wheelchair), and such can make someone identifiable without seeing a face.

You'll find lots of variations in the agency on property releases and when they're needed. Similar story.

If you have releases or can get them, supply them. If you can't and you love the image, perhaps try editorial licenses vs. commercial.

Listen to Sean!  he's correct!

I am still very new at this and just learning the ropes.  Could you give me an explanation for the difference between Editorial and Commercial.  I have read some descriptions, but I still don't get it.  If you sell a photos and some used it , that seems like it is one in the same.  How does it being marked Editorial make it different? Thanks.

Editorial files can only be used editorially, for example in a newspaper, magazine or textbook, guide book etc.
Commercial files can be used commercially, for example to advertise goods or services.

Sometimes it can be up to the agency, for example iS specifically doesn't (or at least didn't used to) allow editorial files to be used in advertorials, Alamy seems to allow that.