I think the confusion is caused by Microsoft using ActiveSync across two different types of product.
I'm guessing you were thinking about desktop ActiveSync which you install on your PC and which communicates with the phone via Bluetooth or USB (it used to work with WiFi too, but not any more). This lets you sync contacts, mail, calendars, etc to your Outlook client but also lets you explore the device's file system, install apps, etc, etc.
What the iPhone supports is officially known as "Microsoft Exchange ActiveSync Direct Push" which syncs Calendars, Mail and Contacts directly with the exchange server and doesn't require any software on the desktop.