Tool Box on Tow Truck ???

We have a Highwayman tool box plus a HighwaymanCompanion box. They are below the truck rails and we have had them for a long time and they hold up well. We have to be careful to make sure we clear the companion box when hitching/unhitching but normally we encounter no problems at all. We are full timers and my spouse carries lots of tools.

No---Had the same combo and tool box was no problem!!

HighwayProducts are TOP CABIN.

New this is over $1,000, I was lucky found on CL for $350. 30" front to back.

There are a variety of manufacturers that make toolbox/chest that sit on the floor of the bed and are flush with the top rails.
such as this one
https://www.deezee.com/product/red-label-fifth-wheel-utility-chest-black/
or here are a couple other styles
https://www.pickupspecialties.com/toolboxes/Unique/5th_wheel_fifth_wheel_tool_boxes_unique.html

I have a headache rack on my truck and chose to do a shorter rv style (like the third picture in the second link) that sits on the floor but I wanted the bed space so I fabbed a frame out of unistrut that I attached to my headache rack mounts and my shorter box is up off the floor so I can still haul long things on the bed floor or put smaller things under it yet it is flush with the bed rails.
There are many manufacturers and quality levels. Previously I had a Dee Zee box in my old truck that is still going after 15 years. The new truck is sporting a Pro Tech box. While definitely nicer than the DeeZee ever was it was also twice the price.

The wise thing is to replace your tool box with on flush to the rails or slightly below. Mine sits about an inch below, and I also have a roll up Tonneau cover.

I damaged the front of my 5th wheel on a sharp turn with a box that protruded about 2 1/2" above the sides of the pickup. I may have been on slightly unlevel ground too. I gave that box away and got one that is flush with the pickup sides. I have short bed and a slider hitch.

Highway Products make several that are flush with the bed rails. I have a long bed, and have their Companion model that goes just behind the tailgate.

Shouldn't be a problem - at least not for me.