CMs on the phone in both Orlando and Anaheim are notoriously bad at knowing the actual operations inside the parks... It's really too bad, but it's not uncommon to get wrong answers on the phones.
carlbarry, from what I've read, if your WDW ticket is a hopper, your DLR one-day ticket will be a hopper.
One Magic Morning is given to those with normal 3+ day DLR tickets. You will be exchanging your days one day at a time, so you will not have a multiday ticket. However, Magic Morning is ALSO given to those staying onsite; you can attend it each day MM is offered during your onsite stay, including the day of checkin (if offered and you're there early enough) and checkout (if offered), as long as you have admission. So if you're staying onsite, you would get your one-day ticket that morning, then you would show admission AND your room keycard (aka "key to the magic" at DLR) to get the MM.
Jozymouse, correct. If you want to use that one-day ticket, you'd exchange it for a one day ticket, then the rest of your stay you would need to buy DLR tickets. If it's one of the tickets you got with a package, when you had other admission for WDW, and it's NEVER been used, it might be better for you financially to just save it, and upgrade it on a future WDW trip, where you would get the value put towards a WDW ticket.