Many will not agree with me but I believe that sharing an alternative view is important here. I am speaking primarily in reference to commodity hardware. When proprietary and non x86 is in scope, things change quite a bit.
If the OEM discovers you're using your own hardware in a server, they might attempt to not support it. However, it is often easy enough to remove it for the purpose of troubleshooting. Realistically, if you are dealing with business support, usually you do not have to go through asinine troubleshooting that you would with consumer support. However, if you did not example a high technical level, you might.
You have hardware people out there that only buy hard drives on a company's spec sheet. In most cases, this level of detail is going to be excessive. This used to matter more. Depending on the hardware in question, you might encounter more fickle controllers or mainboards but typically if they share the same standard interfaces it works. I've known Intel OEM servers to be fickle occasionally but this does not happen very often.
In certain IT shops, you will have a management ethos where they attempt to isolate accountability outside of the IT department. This is often done with support contracts from large vendors. This is more difficult to do if you do not follow the vendor's support requirements to the letter.
If the staff in your IT department is less experienced with hardware, it's easy to buy what the OEM gives you and know it will work. This is a benefit for many as well.
The way I look at it is that you're paying a premium for intangible benefits. Those intangible benefits are more valuable for some than others. In a smaller shop with limited budget, I would stretch it as far as I could.
Now, if you have an existing RAID you should certainly do you best to match the drive manufacture and model. Mis-matching drives has performance implications and is generally unwise.