I kinda have to agree with mirrornl and I don't think it's splitting hairs or being unreasonable to point it out. The links on those pages are actually content on those pages. I'd say that the nursing site he's talking about must have enough trust and power that small bits of content placed on the page can rank - and yes, those links are small bits of content. OP did say that "several" of the lottery-related keywords were ranking, so to me, that means "not all of them". If the "several" were not overly-competitive, and the nursing site has enough trust, I can see how adding "links which are also content on the page" could cause the site to rank for those phrases.