"Refugees in New Zealand often avail themselves of these benefits. The 2004 study asked about the primary source of income in the last two weeks for “established refugees”, who had been in the country for about five years. Seventy-eight percent of respondents declared benefits were the primary income support, while only 19 percent pointed to wages and one percent to self-employment."
Unfortunately I cannot find more recent data.
The last edition of Benefit Receipt of Recent Migrants to NZ was issued in 2008. At that time overall dependence was falling due to the strong economy but refugee reliance on the sickness benefit and DPB was growing.
I am not against raising the quota but NZ does refugees no favours with easy access to ongoing benefits (hence the contrast with the US as per graph above).