Trying to justify perception and stating it exists are two different things. I can speak to both. It definitely exists and the reason it exists is due to verifiable information.

Your statistical analysis cannot disprove perception because people are more likely to accept anecdotal evidence. That is just human nature.

You can definitely fight back with anecdotal information yourself (ie: My relatives traveled to the US and has a splendid time with no problems) but trying to sway people with statistics is a non-starter for a lot of people.