I've now heard back from Verizon, which told me:
"The Verizon model of the Galaxy S III will be global ready for GSM roaming after a software update that will be pushed sometime after launch. After the phone gets the software update to be global ready, customers don't need to call customer service to have it unlocked if they wish to use a local SIM while traveling. They can also call Verizon to have an international data plan added if they'd like."
That's nice to hear, that you won't have to call in to unlock the phone for use abroad. I'm not sure if that means, however, if a US-based SIM for AT&T or T-Mobile will work. Checking again!