There are some low-wattage Seasonic and FSP PSUs that are actually good for more than their labeled wattage, not that running that way for long is a particularly good idea (and I think they're 300W, which would be enough since the +12V rails are strong).
Anything else though, I would not trust in the absence of a competent technical review (e.g. with load testing, waveform analysis, etc).
Assuming the PSU is of even modest quality (e.g. not Bestec), you should have no trouble with a HD5670.