The archive's entry here is one evening and one line. Spielberg brought the film to a White House screening room and showed it to the President, the First Lady and their guests, among whom the account names Sandra Day O'Connor and Neil Armstrong. When it finished, Reagan is said to have told the room that a number of people present knew everything on the screen was "absolutely true". The telling makes a point of the delivery. He is said to have given the line without smiling before moving on to a joke about the length of the end credits. The fact sheet dates the screening only to a year.
What is on the record
Almost nothing, and the entry should be read accordingly. One telling. One video. One reporting channel. No documents, no recording, no transcript. The four resolved claimants are the people named as being in the room rather than four people who have described the evening. The remark reaches the archive as an anecdote about what a man said at a private screening, and the archive holds no independent version of it.
Two readings sit side by side and the file settles neither. A president saying something briefly and seriously to a room he trusted, or a host being wry to guests who had just watched a film about a spacecraft. The account's insistence that he was not smiling is the teller's reading of a face, not a fact about the evening. This is also not a sighting. It carries one motif, government secrecy, and its whole interest lies in who is alleged to have said what.
Why it sits where it does
The entry grades L3 on the number of people named as present, but by the archive's own tier language a single channel is far thinner footing than that number implies. There is no document tier to climb to and nothing here that could be tested. What Reagan meant, if the line was said at all, is not resolved here.