I've requested a read-only access to VMWare infrastructure without much success. I feel that I should provide irrefutable and clear for non-technical people (company's management) proofs and illustrations why I need such access.
What are they?
There are none. You are not going to find anything that can show on paper proof that you need access. There may be scenarios that you can show where it can prove beneficial in turnaround time (or ROI) for solving an issue, especially in a mission critical server. However that is all based on opinion.
I have supported SQL Server VOEs for a handful of years now and have not been provided the read access through VMWare tools. I have one particular environment where I have direct access through VSphere but that is only because that is the only direct access to the server that is available because of the network location I work from. I can say that being able to see that data from VMware is handy, but it is only for two or three servers. If I really want to get the configuration and performance information on a VMWare infrastructure I can just go to the database that stores it, as this is usually a SQL Server database.
To the answer that mentioned Perfmon metrics are not accurate, that is not true at all. There are a few counters that may be off and not show the true activity, like some disk counters, but overall Perfmon is going to show you how the guest OS is operating. There are tail signs that if the underlying host is pulling resources away you will see this through performance counters. This is data I use as ammunition to the VMware admins to explain why I see such and such behavior. The particular counters pointed out in the question are actually only available if enabled through VMWare Tools. Those are special ones that can be very helpful, but I general don't see them.
As well not having that access shows you can work with other members of the team in order to solve a problem. If you require access simply because you do not have a desire to work with them, then it is a personal problem that you have to work out yourself.