That statement is too broad. Consider the following situation. Alan buys a home which he then leases to Becky. Becky in turn subleases the home to Carl. Certainly Alan, who owns the property and has a basis in the structure may depreciate it. But while Becky's lease to Carl is a rental arrangement too, Becky has no depreciation deductions because she does not own the property and has no basis in it. So it is not always the case that rental income means that depreciation deductions are available to the lessor.
So in order to answer the question whether depreciation is available here the issue as I see it would be whether the timeshare buyer receives an actual interest in the property itself, such that he or she has a basis in the property that he or she may depreciate. That will turn on the details of the timeshare deal.