Does systematic search makes someone a true author for a systematic review?
Given the sparseness of the details, its rather difficult to provide specific advice. Here are a few thoughts from someone whose performed systematic reviews for last 30 years, having led teams of reviewers and review programmes, and having participated in the Cochrane Collaboration since its early days:


Performing a systematic review on your own is frowned upon nowadays. In the first place, there needs to be a good balance of content, methods and consumer skills and its very rare to possess all this is one person. In the second place, you'll be making decisions that need to be validated somehow. For example, you are choosing the studies to include and exclude. This is a crucial step and requires another set of eyes with agreements often being resolved by another (third) person.
Searching is a specialist area where research librarians often become involved. It can be the case that someone is on the authorship list not only because they've done the work, but because they can stand by that work. In addition, in the case in which reviewers seek information or modification of your search strategy, the search specialist can handle these issues without breaking a sweat.
If your contributor meets the definition of authorship, he is right to expect it.