The furnace does not need a local fuse box, but will have a circuit breaker or fuse on its power supply. I think what they may be talking about is something more like an actual surge suppressor. There are other devices, and I have one on my system, that monitor the quality of the power and prevent the thing from running if the power is funky. For example, the box I have will prevent the motors (and a/c compressor) from running for a few minutes after the power is supplied. Then, it monitors the line voltage for brown-outs or spikes, and prevents the system from running for a user specified time-out. If you have a power outage, when they turn it back on, the power can be very dirty for anywhere from a few seconds to minutes. This box solves that. The one I have is made by (I think) ICD and cost me about $80 wholesale at the time. I bought it from www.grainger.com . I installed it. the dealer wanted $180 to supply and install it. For general power conditioning, I also have a whole-house surge suppressor on my power panel. It doesn't do that much for internally generated power noise and spikes, but helps from those that come from outside the house.
So, do you need one? Depends somewhat on how stable your power is and how paranoid you are. A fuse, is not going to help one way or the other, since the thing must be coming from your power panel which already has one. Now, local codes often require a local switch to disconnect the thing, and that could be an additional CB or fuse, but it could just as easily be an on/off switch. It would depend somewhat on how far away the power panel was which might be preferable.