Add-ADPermission cmdlet is used to provide permission to Active directory object.  This article explains you how to provide Access Exchange 2007 Database .  Below command sets permission on the Exchange Mailbox Stores and enables the AdminAccount to access uses mailboxes to  view, move, and delete messages, etc 

Get-MailboxDatabase | Add-ADPermission -User domain\Adminaccount –ExtendedRights ms-Exch-Store-Admin

Above command should workd prefectly fine, If you get any errors in executing above command then you may have to do some work around solution to set this

Add-Adpermission -identity “CN=InformationStore,CN=Exchange2007name,CN=Servers,CN=Exchange Administrative Group,CN=Administrative Groups,CN=company,CN=Microsoft Exchange,CN=Services,CN=Configuration,DC=Domain,DC=com” -User “Domain\adminAccount” –ExtendedRights ms-Exch-Store-Admin

Above command helps you the fix the problem. you may have to provide AD Distinguished Name for the Informatio store of the specific server to provide Extended Rights on access to all the Database of the specific the Exchange server. To Provide access to Individual Storage gropue then you may have to try something link this

Add-Adpermission -identity “SG=StorageGroupname,CN=InformationStore,CN=Exchange2007,CN=Servers,CN=Exchange Administrative Group,CN=Administrative Groups,CN=Our Company,CN=Microsoft Exchange,CN=Services,CN=Configuration,DC=myDomain,DC=com” -User “Domain\adminAccount” –ExtendedRights ms-Exch-Store-Admin

Add-Adpermission -identity “CN=Databasename,CN=StorageGroupname,CN=InformationStore,CN=Exchange2007,CN=Servers,CN=Exchange Administrative Group,CN=Administrative Groups,CN=Our Company,CN=Microsoft Exchange,CN=Services,CN=Configuration,DC=myDomain,DC=com” -User “Domain\adminAccount” –ExtendedRights ms-Exch-Store-Admin