Not sure which part of that is an assumption. I didn't say you said anything. I simply explained the things the way they are and tried to rationalize the canon material as logically as I can. Yes, the WSM title is the ultimate proof that Mihawk is stronger than Shanks until we get some kind of confirmation that suggests Shanks is stronger than Mihawk or that Shanks isn't a swordsman. Kaido is stronger than Shanks because he's the WSC. WB was stronger than Shanks because he was the WSM. So the same logic applies here.
Sure, titles aren't always absolutes but we must stick with the titles as long as we don't have anything to go by besides the titles. Literally, every single pirate-related title/position/epithet reputation in OP. The PK title was literally a folk tale. Is the title fake? No. Once again, you're not giving any value to the author's intentions with the character. Oda wanted Roger to be the PK so he made him one in actuality; he wanted WB to be the WSM and he made it true; Mihawk is supposed to be the second most important character's ultimate goal. Why'd he created a fake title for Mihawk of all things? If Mihawk isn't the WSM in actuality, then Zoro's entire goal is pointless.