There is an important distinction between Products and I.T.
Remember that the Product Team is responsible for technology systems and tools -- such as the CRM and website -- that could potentially go any direction. Thus they require a smart, informed roadmap to ensure their development matches the organization's priorities.
By contrast, in our view I.T. is a more of an operations function. It focuses on technology systems that may be complex, but generally don't require the creation of a roadmap. As an oversimplification, your IT systems either work or they don't.
Examples of internal I.T. functions include purchasing and setting up computers, networks and internet access, software and installation, email accounts administration (such as Google Apps for Work), password management, web domain registration and accounts, web hosting accounts, and all technology-related billing and payment.
The Product Team must not be pulled into I.T. roles, even if they seem to be more "tech savvy" than other people in the organization. Otherwise the I.T. workload will quickly overwhelm the product team's ability to do their primary jobs. Eyes will be taken off the ball, and crucial balls will be dropped. This defeats the entire purpose and mandate of the team!
Fortunately, a viable I.T. option for some organizations are external tech support providers, to whom you can outsource much of the basic I.T. support, such as issues involving computers, software, printers, networks, internet, and advanced tech support.
That way you keep your product team's eyes on the prize where it belongs.