There's actually a current idiosyncrasy (bug, imo) with Analytic's share features due to the integration of the Admin Console. Many assets (projects, segments, etc.) can only be shared with individual users or, if a product admin, with product profiles. So even if user groups are defined within the Admin Console, they cannot be selected to share content. So unless each group of users is defined under their own product profile, sharing this content will be accessible to everyone else in the product profile.
Not sure if it directly answers your question about scheduled reports, but I've posted a related feature request, here.