Is A Server, A Server and Only A Server?

How important is it to know about customers business processes when running IT Infrastructure services as a service provider? And the reference is in terms of what application development and maintenance providers need to know, which is relatively a no brainer. The application development and maintenance service provider needs to have a deep understanding of customers business processes to be able to deliver with an appreciation of the impact on the customer's business. For IT Infrastructure though many say a server is a server is a server. Or is it?

There is no denying that knowing customers business is always good if not essential but the question is how much does a service improve in terms of IT Infrastructure services with a knowledge of customers business. Personally I think that if rules exist to priortize incidents, list critical environments in various tiers of service and there is an application to server mapping with critical ones defined then knowing customers business will still be good but it may not result in major differences. There are still areas like batch job management where this information may be more crucial but it may not be making a very big impact overall.