What's the explanation for my product permission issue in a Drupal Commerce view?
Below is another recommendation to address your "... I went to the permissions config page, and I checked the permission "View any product of any type" for anonymous and authenticated users" ... and your "So I do not know if I'm doing things correctly".

Have a look at the (old) Drupal Commerce issue "Views results empty for unprivileged user when using Relationship: Content: Referenced Product". Especially what's written in comment nr 158, i.e.:


  edit your View: > "Advanced" > "Query settings" : check "Disable Query Rewriting"


So instead of granting that permission (so that "normal users and anonymous can see the view correctly", as in your question), it may be sufficient to just adapt these advanced query settings as mentioned above. If it does, it'll be way better then granting that permission with that scary warning.

If you want more info about what the real issue is (and why this is only a work around), then have a look at comment nr 101 of the same issue, which states:


  The issue is not with Commerce. It's a node access issue, and it's triggered when you use a Views Relationship with a node access module (such as OG or Domain Access), and there's no related item the user has access to. The quick work-around is to disable SQL rewriting, which allows the view to get all results and ignore the node_access rules -- of course, this will show content the user should not otherwise have access to.