For the purpose of discussion, in general, there are two kinds of positive reactions to links.
The first class is the reaction to a surge of links that indicates to Google's algorithm that a site is important at this moment in time, like it's newsworthy, a subject of sudden interest, etc. This is short term.
The second class indicates that your peers believe your site is relevant for a particular phrase. This is long term and gets folded in over the course of months.
It sounds like they are exploiting the short term ranking algorithm by building links for the short term then replacing them with a new set. This is a "trick the search engine" type of SEO. It's short term and benefits the SEO company because it keeps the client returning in order to sustain the rankings- which is good for the SEO company doing that work for them. If they're in a competitive industry and don't mind burning a few domains while on the path of big profits then it might be what they need.
But if the company is interested in achieving rankings for the long term, then "tricking" the search engines may not be in their best interest.