Same here. I do wish DH would prioritize those who have been both longer and only contact support when absolutely needed. I have been a customer for 4 years and contact like 2 or 3 times a year.
It is a hit and miss with them. I have at one time had support reply to me within 5 minutes and it went back and forth withing minutes almost like on IM. But then again sometimes it leaves much to be desired.
Regarding the 'policy', yes they do strive to answer support request within 24 hours. If it will cross 24 hours you should receive an automated mail form them asking you to just hang in there for a while due to there back log. If you did not receive this automated reply, than something must be wrong.
I do have this feeling that depending upon the level of ease of your support request the speed would vary. Help on pointers to get things done would be generally faster than asking DreamHost to do something with your account such as updating a core package etc might incur a longer support time. Just a guess.
Here is a snippet from one of my super fast support replies:
Haha, isn't it awesome? Some people wonder why we don't provide IM-based
support but we strive to offer great response times via emails so that
it's not needed. Many also ask the same about phone support, but we
believe we can do things a lot faster and better via email. Besides...
who likes waiting on hold?!