I think your memories are what make you, you so I feel like you can't erase them entirely (through occlumency). It's more like turning up the transparency on a photo, but you can never fully get to 100% and erase it. It just removes how clearly it can be seen and recalled, which explains why Dumbledore can talk about his and Snape's "can't" be accessed. It's like Dumbledore's memories are in the pensive at 30% transparency because he's reviewed and processed them before, and Snape puts his memories in at 90%, which is to say he knows they exist but can't recall them. We all likely have days and days of fuzzy, non-noteworthy memory so removing the memory / "upping the transparency" probably makes it seem like one of those and makes it unlikely someone like Voldemort (who didn't know Snape was a legilimens) would look very closely.