What you need to consider is the "base rate": How many things would innocent people say in the same time period which could, if written down and then scrutinised carefully for anything odd, be construed as odd?
As has been pointed out before you don't need to go beyond this case to find plenty of examples of police saying "odd" things, the roommate Filomena saying "odd" things and Meredith's friends saying "odd" things (oh my God, they changed their story about the time of Meredith's final meal!).
The difference seems to be that when the police, Filomena or Meredith's friends say something "odd", guilters are able to see immediately that a certain number of mistakes are completely natural when fallible people with fallible memories discuss a complicated case. Yet when Amanda or Raffaele say something "odd" they seem to fall into the assumption that innocent people never say anything "odd" because innocent people have perfect memories and never mis-speak, and conclude that because they said something "odd" they are more likely to be guilty.