Working distance is measured from the front of the lens to the subject. For your EF 100mm f/2.8 L IS USM Macro lens the working distance at minimum focus distance (MFD)/full magnification is approximately 133mm.
Focus distance is measured from the subject to the imaging plane (film or sensor). For your EF 100mm f/2.8 L IS USM Macro lens the focus distance at full magnification/MFD is 300mm.
Most lenses' focal lengths are measured when the lens is focused at infinity. As focus distance is reduced, the angle of view provided by the lens often changes. This is what is know as focus breathing. The 300mm MFD of your EF 100mm f/2.8 L IS USM Macro reveals to us that the effective focal length at 1:1 magnification is about 75mm. This is fairly common for a 100mm Macro lens.
Additionally, focal length for a compound lens is approximated from the focal length a single lens would need to be to provide the same amount of magnification. A compound lens is a system of several lenses, usually arranged in groups, that together act as a single lens. Pretty much every commercially available lens for interchangeable lens camera systems are compound lenses. Your EF 100mm f/2.8 L IS Macro has 15 lens elements arranged in 12 groups.
For most wide angle lenses which have a retrofocus design, this theoretical thin lens point is well behind the front of the lens. For telephoto lenses this point is, by definition, in front of the front of the lens.
When focused at the 300mm minimum focus distance (MFD), the front of your EF 100mm f/2.8 L IS USM Macro is about 168mm in front of the sensor. But the field of view and magnification provided by the lens at MFD makes it effectively a 75mm lens at that focus distance. This means a simple 75mm lens would need to be at 150mm in front of the sensor (which also places it at 150mm away from the subject) for 1:1 magnification. This places the effective center point of your EF 100mm f/2.8 Macro about 18mm behind the front of the lens when focused at the MFD.
So I think I missing something, can someone explain where I'm wrong?
When applying formulae such as those in your question, you need to use 75mm for the lens' focal length when it is focused at MFD.