Maybe they want to standardize on HP servers, vSphere for virtualization, RedHat for Linux, Cisco for the data center network, EMC for the storage, and so on.
The specific choices aren't relevant in this argument; the underlying philosophy is what matters.
The newer thinking in this arena is pre-integrated stacks: converged (e.g. VCE Vblocks, HP CI, etc.) or perhaps some of the newer hyperconverged offerings (e.g. VMware's EVO, Nutanix, etc.). Less effort all around thanks to a modicum of integration, but still a generic stack by any other name.
So, let me ask a clarifying question: what are the most important and demanding workloads in your landscape?
I'm guessing it's databases, and the applications that use them. Might it make sense to think in terms of *optimized* stacks for these crown jewels vs. generic ones?
If your business is heavily invested in databases, maybe mainstream generic infrastructure thinking isn't doing you any favors.