Their "pliers" are not needle nose pliers from the hardware store, they are most likely specialty tools.
Example, take a look at the tools at "pen tooling."
On a hardware store plier with teeth, the teeth will imprint/mar the nib. You need a plier without teeth, or at least be padded enough that the teeth won't mar the nib.
A plier allows the skilled tech to do easier and faster what would be done with the fingers.
Again, a plier magnifies leverage and eliminates feedback. So you REALLY have to know what you are doing.
That is the same reason I do NOT recommend newbies use a "section plier." It is too easy to break the barrel or completely shear a pen in half.
The tool you did not mention is a nib block.
For hobby use, get the affordable $30 acrylic nib block, not the EXPENSIVE $200+ metal nib blocks.
Burnishers are DiY or commercial. If you look creatively at some kitchen utensils, you can use some of them as burnishers.
You have to PRACTICE A LOT, to learn how to use a nib block to straighten a nib. There is a lot of learn by trial and error.