Would a perfectly reflecting full Moon be just as bright as the Sun?

I've read that the full Moon has a magnitude of about -13 and an albedo of about 3%. That implies that if the lunar disk reflected 100% of sunlight it would appear more than 30 times as bright, or about magnitude -17. But since it has the same angular diameter as the Sun, shouldn't a perfectly reflecting full Moon be just as bright as the Sun?

Full Moon

When the Moon is full, its craters, mountains, and other surface features appear muted because the high Sun casts no shadows as seen from our earthbound perspective.
Gary Seronik

There's no single value for the Moon's albedo (reflectivity). The bright highlands have a range of 11-18%, whereas the dark maria are 7-10%. And the lunar surface looks more reflective at full Moon (12.5% overall) than it does at other phases. Jeff Medkeff has written an excellent summary (http://jeff.medkeff.com/astro/lunar/) of the problems astronomers face in defining and measuring the Moon's reflectivity.

But even if the lunar soil were perfectly white, the Moon wouldn't be as bright as the Sun (magnitude -27). That's because sunlight striking the Moon is reflected in all directions instead of straight back to us on Earth. If a 2,160-mile-wide flat mirror were placed on the Moon to redirect sunlight toward you on Earth, then the Moon would look as bright as the Sun!

— Roger W. Sinnott