I have cruised from Galveston on the 7-Night Western and 6-Night Western on the Magic. I stayed at the DoubleTree by Hilton at Hobby Airport each time. I took the hotel's shuttle to the airport and then checked-in for Disney transfers on level 1 baggage claim! (They now have an actual desk next to the car rental companies on level 1!).
It's a nice short (45-minute) ride form Hobby to the port. I could not imagine what traffic could be like leaving from IAH (Houston Intercontinental). For a single traveler, the port transfers are the cheapest way.
If you actually look up the Disney transfers, they do allow just "airport" to "port" and back.
http://www.disneywebcontent.com/dcc/1724/fb6b651c69f28210vgnvcm100000d864a8c0rcrd/
You do not need to book your hotel stay through Disney. What the Disney CM was referring to, was the 2 hotels that Disney uses for pre-departure and post-departure stays. If you want to stay in Galveston before and/or after the cruise, the transportation does become more problematic and it is probably better to use the Disney transportation and hotel(s).