You are right! It is tradition to have the www and therefore expected by many. Tradition that is many decades old should not be easily discarded.
At the very least, you may not be capturing the traffic that expects the www. Normally, I would say that you need to choose one or the other, www or non-www, but both should exist with one redirecting to the other. It is often better to redirect non-www to www. This answers the concern over web space, duplicate effort, and duplicate content.
Whoever created that rule likely cannot properly justify the decision without a wealth of valid reasons against to the contrary. In short, it is just a plain 'ole silly [***] thing to say and does the companies website a disservice. It misses the full potential of capturing traffic.