Are you sure that the infrastructure behind Outlook and Office 365's Outlook is sufficiently different? I was under the impression that it's similar if not the same. Compare Outlook:
$ dig mx outlook.com
;; ANSWER SECTION:
outlook.com. 300 IN MX 5 outlook-com.olc.protection.outlook.com.
with my university that is a customer of Outlook on Office 365: $ dig mx uniri.hr
;; ANSWER SECTION:
uniri.hr. 86251 IN MX 0 uniri-hr.mail.protection.outlook.com.