And “appears to have” is lawyer talk for “we don't know that this occurred and can't prove it and absolutely want to make clear that we will not be accountable for claiming it actually happened.”

It's lawyer talk for "We think it happened but we want wriggle room"

It's also lawyer talk for “we’d like the recipient/reader of the document to think it happened, but we don't want accountability, e.g., in the case of a document intended to be made public, for defamation.”

You said "in this context lying is fraud", and that's not the case, which is why lawyer talk for "fraud" is "fraud", not "lying".