Here's the whole section, minus the exceptions for what listed hoods do not have to meet and recirculating systems:
507.1 General. Commercial kitchen exhaust hoods shall
comply with the requirements of this section. Hoods shall be
Type I or II and shall be designed to capture and confine
cooking vapors and residues. A Type I or Type II hood shall
be installed at or above appliances in accordance with Sections
507.2 and 507.3. Where any cooking appliance under a
single hood requires a Type I hood, a Type I hood shall be
installed. Where a Type II hood is required, a Type I or Type
II hood shall be installed. Where a Type I hood is installed,
the installation of the entire system, including the hood,
ducts, exhaust equipment and makeup air system shall comply
with the requirements of Sections 506, 507, 508 and 509.
There is nothing saying that a hood over an appliance that only requires a type II hood is designated as a type II hood, it says the appliance can be under either a type I or a type II.
I know the commentary is not code, but it is a tool to be used to help in interpreting the code. Here's what the commentary says regarding this: "If such type I hood is connected to duct suitable for only type II hood systems, a fire hazard could result. Building owners and tenants could think they have a type I hood system when viewing the hood, not realizing that the hood system is actually a mismatch of a type I hood with ductwork that is not compatible with a type I hood.... If the type I hood was later used with appliances requiring type I hoods, a severe fire hazard would result, unknown to the building owner or tenants. The code intends to prohibit the installation of a system that is misleading as to its capabilities, application , and purpose."