My guess would be that these services were provided by devices that were connected directly to the servers or were in the same area.

This would be contrasted with networked solutions where you may be in Berlin, but your email server is in Tokyo and the printer server is in New Dehli.

My guess from the USA.

This appears to be a term coined by Dell. It doesn't appear otherwise, that I can tell. It appears that Dell does not intend to get into advanced professional services (network design and installation services, application development, network management, etc.) and instead intends to continue offering services that relate closely to the sale and support of computer hardware.

The following are captured from http://www.google.com/search?hl=en&lr=&q=services "close to ... :
"Dell services currently accounts for $4bn of the company's $35bn revenue, although Claman admitted most of that is from 'close to the box' basic services such as warranties. He predicted services will have to become a much bigger part of Dell's income in the future."

"Leitch says Dell was not offering high-end consultancy but rather “close to the box” services. Such services would involve customers choosing from a menu of services within a “standard operating environment”. The services would be delivered using Dell’s sales staff and consultants [I understand that these are "consultants" of the type who help you decide which PC is best for your needs], plus logistics staff in Auckland, Wellington and Christchurch."

"Dell said Wednesday services was "one of the fastest growing" parts of his Round Rock, Texas, business, with about half its revenue derived from "close-to-the-box" services such as support and maintenance and half from professional services, such as technical consulting, network design and implementation and the like."