I am not quite sure if you are able to put company in the inamate or animate category and neither if this adequate to choose between who and that.
In this case I would assume to take it as animate (and "humanoid"):
The company is able to trade, to bargain etc. Inanimate assumes it would not be able to do that. Therefore company refers to the management or the representative(s) in this case.
Categorizing as humanoid and in-humanoid or the ability to take decisions ("conscious mind") as a guideline is preferable. E.g. animals you can use both who and that but they are clearly animated. If you see them having a conscious mind as humans (sometimes) have, is to be discussed in a philosophical way.
He avoided the dog who bites.
He did catch the fish that looked injured.
He avoided the dog that bites.
He did catch the fish who looked injured.
Besides on "quick and dirty tips" is a post with a hint, that some authors in the past used "that" even with humans as reference and a quote of
American Heritage Dictionary stating
It is entirely acceptable to write either the man that wanted to talk to you, or the man who wanted to talk to you.
so it is not really clear at all.