If you create a report for which access is set as "personal" and you share it by "send as email" does the report then appear in the person's Reports & Charts section? What report group would it appear under, "Common", or?
What if you just give them the URL to the report?
If you have created a section, do those report groups appear for other users if some of those reports have been shared with them? Or which section does it appear in?