I'd actually argue that the opposite is true-- most rack-mountable machines are designed and purpose-built to be server computers. Today's modern rack-mountable servers are designed with energy efficiency in mind, whereas "tower" computers, while potentially still designed with energy efficiency in mind, aren't typically designed for server workloads.
In a hypothetical scenario with all things being equal between two machines except for the case and mounting hardware basic physics says that the heat output of both machines will be the same. Racks, however, have the advantage of allowing you to construct "hot" and "cold" aisles in the datacenter-- that is, rows of machines with their fans all pointing in the same direction sending their hot exhaust air directly into ducts while pulling cool intake air from the other side of the rack. This isolation typically allows the HVAC system to operate in the most efficient manner. Tower cases typically aren't amenable to this kind of isolation and you end up with intake air being "recycled" exhaust air. Concentrating the heat is a Good Thing(tm) if the heat can be efficiently ducted away from the servers.
If the company only has a few server computers they're not going to have an appreciable difference in server energy usage expense (assuming that the "tower" servers they're using are as energy-efficient as equivalent rack servers-- "build it yourself" white box "tower" server computers will not achieve anything close to the efficiency of a purpose-build rack server computer from a major manufacturer).
It sounds like they didn't have enough machines (or a sufficiently small space) to worry about active cooling and they were just getting by with passive cooling. That's not a function of their using "tower" servers, but rather a function of the size of the room, airflow, ambient air temperature, and the small number of machines outputting heat. With any quantity of servers or a confined space with poor airflow, though, they would need active cooling and, at that point, there are major efficiency gains that can be had by using rack mountable equipment and ducting the exhaust properly.
Of course, cooling and efficiency are only part of the equation. Technician hours are expensive, and nice things like integrated cable management, telescoping rails, cable management arms (I like them, personally), and the general "designed for servicing" nature of quality rack-mountable server gear makes for less time spent when servicing failed components. Try quickly disconnecting a "tower" server from a mass of tangled cables (as I've so frequently found behind the typical "tower servers stacked on wire racks" installations).