question about the shoes

i want to start by saying i believe lindsay is 100% criminally responsible, she did it and was of sound mind when she did so.

that being said, i am curious what the patrick conspiracy theorists are implying with him having different shoes in CVS vs the restaurant. like, if the shoes are different, what does it mean? why does it matter? why does that mean he killed the kids? are they arguing that it is a whole elaborate coverup with the cops and the owners of the facilites? why would they do that??

basically what does him changing shoes have to do with anything?? not trying to argue just genuinely trying to understand