Nope!
It's not any one thing but a combinating of many... but developing links "if nothing else is available" does help a great deal... unfortuately it doesn't work that way for:
1. All websites,
2. Targetting all keywords and all keyphrases,
3. In all industries, and
4. Targetting all markets...
One reason many self-proclaimed "experts" get into hot water with clients... success on one site, on specific phrases, to one industry, targetting one market isn't a successful track record - but a diseater waiting to happen.
In your specific example: the non-profit organization "
status" produced that
SEO "expert" look - not an expert
SEO.