Good point. Which is most likely what he did right since it would be nearly impossible to rank for a high comp keyword with only brand anchors???
I have not tested this but in theory it is possible as no penalty will be activated for over optimised anchor text for the target keywords where as the links pointing to it still pass power and Google can work out what the site is about from its own onpage text along with the on page text of the sites linking to it.
I am guessing that the keywords you are aiming for are things like "limousine service los angeles", "limo service los angeles" and "los angeles limo service" like their site has good rankings on?
Personally I don't think these are high comp keywords. I had a quick look and the Yelp page doesn't have any visible strong links so I would guess it is only there from its domain authority and on page. Sorry if one of these are your sites but lalimo.com, fivediamondslimo.com, la-limo.com, klsla.com and losangeleslimosservicesca.anytimelimousines.com don't seem to have much when it comes to off page SEO.
The only strong sites I could see at first glance are crownlimola.com, americanlimos.org, crownlimos.com and lalimorental.com. Out of those sites both of the crown sites are probably what I would class as the strongest of the top 10 in my opinion anyway.
Additionally americanlimos.org and lalimorental look like they may have used black hat techniques or spam to get up there already so they may have hidden links that I can't see.
In addition to that they are pulling Google traffic from branding keywords such as crown limos, crown limousine and crown limousine la. I would imagine this would give them a boost also in Google as Google can see people are searching for them and clicking on their website with branding searches. Without knowing your site I can't tell if this is the same or not.