The power coming out of a generator (at least mine, since it is not a very high dollar generator) is too dirty (i.e. too many pressure surges). The Helix DBS-1000 has too many built-in error codes to run of a generator. The Helix 1500 watt has no error codes, and I think this is why it will work on the generator power. Maybe some have had better luck than me, but I tried to run all 12 of my Helix DBS-1000's in 2005 after Hurricane Katrina, and was never able to get them to work.
I hope that is explaination enough. Let me know if you need me to expound more.