Respectfully, why jimderod wants to downgrade is irrelevent. He/she is asking "Can it be done?" I am assuming by your answer that you have tried it yourself and have found Win 7 will not recognize Win 8 as a "previous installation?"
In response to your question, "Why did you buy a Windows 8 PC if - for some undisclosed reason - you need a Windows 7 PC? " I would remind you that jimderod may not have had a choice as Microsoft will not usually allow a choice of the operating system on a new computer.
As far as your perspective of "Then you would need a full install file of the first OS," I would, again, respectfully submit to you that Win98 SE, is, in fact, a full OS for this purpose. I tried it myself and found one need not concern oneself with the computer's (too fast a CPU, too large a disk, motherboard not compatible) hardware as it is only a "primer coat" and need not function in any manner, just be loaded to be recognized as a "previous Windows installation."
Your statement "The first thing to do is to fully erase (with a program like KILLDISK or DBAN) the hard disk of the PC/laptop" is absolutely correct and serves as excellent guidance to jimderod's question.
However, jimderod did not ask for "the easiest way is to install the full (retail) version of Windows 7," as this would also be the most expensive way to go.
Again, he/she asked if it could be done.
Let me use this analogy... When we moved into our present home, we wanted to put "Sky Lites" on our metal roof. The contractor said, "Certainly. Almost anything can be done....for a price."
Of course, jimderod can downgrade (the easiest way- as you suggested) his/her OS... for a price."
I just don't think that's what jimderod was really asking. I could be wrong.