so let’s look at both sentences. When Americans say sorry, they mostly mean it. -This means that when Americans say sorry, they usually mean it; or they mean it, but not wholeheartedly. But, at least to British ears, they (Americans) don’t necessarily mean anything else they say. -This means that British people don’t think Americans mean what they say all the time. They might mean it, and they might not. So what an American says might be true, or it might not. Hope that helps :)

To put it simply, it means that British people find Americans insincere. Americans and British people are pretty different culturally - Americans tend to be much more enthusiastic about things which might sound false or insincere to British people. British people are normally a little pessimistic and not really enthusiastic about things. So Americans will often say something is 'awesome' or 'amazing' but British people will say the same thing is 'nice' or 'not bad'. Depending on the context, I'm thinking there may be another layer here too. British people say 'sorry' all the time, even when we don't mean it or when it's not necessary. So there could be an extra meaning here that Americans are sincere in their apologies, but British people are not.