It's not illegal to make false statements in this context. It's illegal to knowingly and willfully make false statements. If later, the author said something l

It's not illegal to make false statements in this context. It's illegal to knowingly and willfully make false statements. If later, the author said something like "I was talking to my roommate in his room just before you guys knocked on the door", then he might be charged with a felony. But the statement by itself was fine, even if false. 18 U.S. Code § 1001