I can back that up from personal experience.
I was one of three volunteer members of a jump team that went into St. Thomas, U.S.V.I., the day after Hurricane Hugo. I had colleagues who were waiting to go into Charleston.
Within 45 minutes of landing, or an airplane we had to privately charter, my team established the only communications the islands had for quite some time. We worked for the Red Cross, but served almost exclusively for the Virgin Islands Territory Emergency Management Agency, the counterpart to what we know as FEMA on the mainland.
We communicated on a high frequency band with all parts of the mainland at various times of the day as the band allowed, seeking emergency supplies and communications equipment. We also communicated via data connections through our ham radios. One higher frequencies we passed traffic from St. Thomas to Puerto Rico.
All our communicationing was done on our own equipment, none supplied by the Red Cross or VITEMA.
The island people were very appreciative, and it was quite rewarding for my two teammates and me. I heard the same from hands who volunteered in other areas in the Hugo disaster and also in later disasters.
I could go on for pages on our activities, but that is why we were there, to do what needed to be done.
For information on other disaster relief by hams, check arrl.org and hunt around that site. Also, you an ask the American Radio Relay League (ARRL) to set up a speaker for one of your groups meetings. One things hams like to do is talk.
Here's one link I could find quickly.
http://www.arrl.org/pio/press_releases/2007/0926b.html