[SalesForce] Insufficient Privileges as System Administrator on Opportunity

So it's not a real contact, it's a person account (means you have Contact OWD set to "Controlled by parent")...

Still, same logic as described in my comment applies - click the [Sharing] button, expand the list and check if that user is present on the list for that record.

If he isn't - you'll have to fix sharing by doing any of these:

• changing OWD for Accounts to Public Read Only or better
• creating a sharing rule
• making him owner of that person account
• adding an entry in AccountShare table (in UI it's under the Sharing button) or making him an Account Team Member
• if the view page is overridden with visualforce page + controller - you could try using "without sharing" in the class definition.

Pick carefully, the first 3 solutions can have huge impact on your organization's data visibility.

whether members of the same role see each other's accounts, depends on the org wide default set for account object in Sharing Settings. If it is public then members of the same role should be able see each other's accounts.

If it is Private, then No. the owner of child accounts should either manually share the accounts or a sharing rule with proper criteria has to be built or some apex code should be written to explicitly code this.

If territory management is enabled then visibility depends on territories assigned. Yes it also depends on role hierarchy.

You can check complete access to the account using the Sharing button on detail page. It should be visible to an admin. you might have to add it to layout if required.

Access to Parent Account doesn't automatically grant access to child accounts. Although names of the account will be visible in Account Hierarchy page, clicking on account will result in error.