[SalesForce] Cannot Edit the Object Permission for Standard User Profile or for any Profile while logged in as System Administrator in Developer Sandbox

Actually, the PermissionSet SObject has a field in it called IsOwnedByProfile. Take a look at this blog post by Adam Torman, http://blogs.developerforce.com/engineering/2012/06/using-soql-to-determine-your-users-permissions-2.html:

This field determines whether a permission set is a custom one or if it is parented by a profile. This is made possible because for every profile, there is one underlying permission set. That way, permissions layer equally across permission sets without having to treat a profile differently.

So, if you want to find the CRUD permissions of a profile you can do something like this:

SELECT Id, SObjectType, PermissionsRead, PermissionsCreate
FROM ObjectPermissions
WHERE parentid in (select id from permissionset where
PermissionSet.Profile.Name = 'System Administrator')

I just ran into a very similar issue with Opportunity and a custom object that had a Master-Detail relationship back to Opportunity.

I was attempting to insert an ObjectPermissions record against Opportunity for a particular ParentId PermissionSet and got the following error:

Id permissionSetId = //... Some existing Permission Set gets looked up. 

// Note the omission of PermissionsViewAllRecords = true
ObjectPermissions opportunityObjectReadPermission = new ObjectPermissions(SobjectType = 'Opportunity',
                                                        PermissionsCreate = false,
                                                        PermissionsDelete = false,
                                                        PermissionsEdit = false,
                                                        PermissionsRead = true
                                                    );
opportunityObjectReadPermission.ParentId = permissionSetId;
insert opportunityObjectReadPermission;

System.DmlException: Insert failed. First exception on row 0; first error: FIELD_INTEGRITY_EXCEPTION, Permission Read All ChildCustomObject__c depends on permission(s): Read All Opportunity: []

It turned out there was already an ObjectPermissions record for ChildCustomObject__c that had PermissionsViewAllRecords = true. For that to exist there was already a corresponding ObjectPermissions for Opportunity with the same view all records setting. That makes sense:

If you are going to allow the view all records permission on the detail object in a master-detail relationship you also need to grant it on the master object.

This is applicable to your deployment issue as well. You can't deploy permissions for the child/detail sObject without also deploying the required permissions to the master sObject.