If what the writer said was strictly true, Apple would be having a little security freakout about how Muse managed to bypass this OS control. My assumption is that the writer did not understand everything he was granting it permission to do, so he legitimately believes that he didn't grant it those permissions. But he did.

Apple's statement is that the permission is being abused to do things that users do not think are possible.

In this case, Meta explicitly promises that Muse will not read your messages even after you grant it disk permissions.