Stock has the potential to be more viscous than broth (a density issue). Commercial stock may have less gelatin - it likely is not as viscous as home-made stock. It seems like the recommendation for commercial stock is intentional. I'm happy to reach out to Ball if you would like further confirmation. 

-Nicole 

Update - The NCHFP Director and I did end up reaching out to Ball/Newell Brands directly about this question. Please see the email to them below. I will reach back out when Stephen responds. 

[Stephen, during a recent conversation with Nicole she raised a question regarding the use of home-canned bone broth versus commercial options in recipes, specifically citing limitations with homemade chicken, beef, or vegetable broths for your French onion soup.
My understanding is that the restriction on homemade chicken, beef, or vegetable broths, while allowing home-canned bone broth, may relate partially to the fat content in the meat-based broths and the consistency (thickness) of vegetable broths based on home preparation methods. Nicole also found an article mentioning gelatinization as a reason.
We are both curious about the reasoning behind these recommendations and would appreciate any insights or explanations you could provide on this topic.]

I am going to close this Ask Extension question and will respond via email once I have a response back from Ball/Newell Brands. I will start an email thread to keep it at the top of my list. 

-Nicole (Arnold<personal data hidden>)

Response from Ball/Newell Brands: 

[...after some digging I was not able to find a definite answer on this from the notes for this recipes validation.

We have a recipe for home made chicken bone broth that is used in several recipes so that doesn’t seem to be a concern.

My best guess, based on how many of our recipes are chartered, is that the homemade version of beef bone broth was integrated to give an idea for how to use the bone broth in another recipe. Many of the recipes in our books stem from the question “what do I use this recipe I just made for”, the answer being… in another recipe! But in case someone did not have their own broth prepared following our broth recipe or did not want to go through the work of making it, we would usually recommend a store-bough alternative for consistency since there may be un-anticipated additions to other homemade versions. So having both options allows folks to use the beef bone broth they prepared in the French Onion soup, or use a ready alternative. I don’t think the chicken bone broth was deliberately left out, more than likely they were just thinking of the beef one when they wrote this particular recipe.]