Presumably they can't check their internal mail via Gmail, but can via either Outlook or their own corporate webmail interface.
Well, standard Yahoo! Mail has IMAP and POP support, so they could theoretically pull it into Gmail. They could also forward it. But I'm guessing all of those options are a violation of company policies.
The memo appears to be talking specifically about internal corporate email. Did Yahoo! ever sign up for Google Apps? I doubt it, in which case they are probably trying to get people to migrate from Outlook 2007.
Can't Gmail be set to login and use other POP3/IMAP and SMTP accounts?
The first thing I did was to literally scan for that word.