First why a Postdoc would consider a second PhD:
Needless to say, how the existing system treats the Postdocs-Use them, as a cheap labor and throw them. In almost all of the occasions, it is the Professor/Supervisor who is benefitted.
According to Nature article, vacancies in academia is available only for 15% of the Postdocs. In addition to this, comes the problem of Visa and Racism. In France, it is impossible for one to get a job (even in Industry) let alone be called for the interview, without perfect French and a "French" sounding First & Last Name. Yet, French institution lure students from developing countries with their fancy programs. In one of the article on the "invisible" racism in Canada, one even acknowledged that the system is skewed in favour of Canadians (they want the good jobs for Canadians), yet they beckon PhD's and postdocs, from all over the world. Then, say the education is not enough, forcing them to work as bartenders and taxi drivers. Nature (Journal) itself points to some postdocs to have taken up the job of a forklift. Personally, I know a postdoc ending up as a stay-at-home Dad...And in almost all cases, none even spares a moment to think about the future and families of their postdocs or help them acquire skillsets that could help them move to industries, in the worst case scenario. Neither, opportunities in entrepreneurship is supported (National Laboratories, for example). In fact, Canada actively discourages it.
So, the best reason I think a person would choose a second PhD is to survive and since, PhD is usually longer than a postdoc could hope to acquire skillsets that could be used in industry and subsequently find a job. Personally, I would urge you to consider the postdoc as you'd be helping him and also prevent another "idiotic" bright student from wasting his life in the name of academic/knowledge pursuits It is a beneficial proposition for you as well, as a postdoc would require less supervision and hence more publications could be achieved for lesser cost...!