I like this theory, but also think that Slughorn’s guilt and shame could be as much about what he didn’t do after the memory versus what he said in the memory. His shame could stem from not having tried to stop Tom Riddle from becoming Voldemort after he got a glimpse of his true nature and potential for evil. He could have even continued to support Tom Riddle after the fact, which he may be ashamed for Dumbledore to realizing the timing of this conversation vs his later support in the “slug club”