Depends what you mean by "the procurement team". People with procurement in their actual job title are glorified paper pushers who's job is to make you think that you need to offer a better price but are actually entirely subordinate to the people who've made the decision to recommend to buy your software.
On the other hand, the level of upper management that tends to make the decision is exactly the sort of person this demo advice applies most for: the people who really don't care about the flexibility of your search function or UX (because they're probably not using it themselves) but are quite impressed when you use it to highlight a solution to a problem unique to their company/sector, and don't actually have time to watch a walkthrough of Feature X but do remember the story about how it saved a company facing similar issues $100k
The article covers a bunch of different stuff - some of which I'd expect buyers to try and dodge, some they won't be so concerned with.
For example, when I hear this bit from the article:
Sales rep: “So, currently your company is losing out on
sales opportunities because leads are falling through
the cracks. [...] how much revenue do you think you’re
missing out on just because of ineffective lead
management?”
[...]
Sales rep: “So we’re talking hundreds of thousands of
dollars in lost deals every year.
What I hear is a sales rep asking "What is the highest price you'll ever pay?"
Revealing this strikes me as an unconventional approach to price negotiation.
I would imagine senior executives at major companies would know such things - be it from their procurement teams, their education, or elsewhere.
Though it can be much easier if you're asking the more sensitive questions as a plausible part of a demo rather than grilling them at the beginning.
e.g.
"So this is how you track your lost deals from each month, and we allow you to use different ways of handling bulk leads and smaller volumes of high value leads. So what sort of number do you think might be falling through the cracks in a typical month?"
[...]
"that definitely sounds like something you'd want the ability to monitor individually. Particularly as earlier you mentioned your typical deal size was at least $10k, so that's over $50k each month that our better lead management system could help you with accurately tracking and following up"
A lot of the time the procurement team can tell the buyer to fuck off, or they'll suggest another software they already have a license for to try first
On the other hand, the level of upper management that tends to make the decision is exactly the sort of person this demo advice applies most for: the people who really don't care about the flexibility of your search function or UX (because they're probably not using it themselves) but are quite impressed when you use it to highlight a solution to a problem unique to their company/sector, and don't actually have time to watch a walkthrough of Feature X but do remember the story about how it saved a company facing similar issues $100k