The mishna in Yoma 3:1 talks about watching for dawn to know if it's time for the morning offering, and then Yoma 3:2 asks:

וְלָמָה הֻצְרְכוּ לְכָךְ, שֶׁפַּעַם אַחַת עָלָה מְאוֹר הַלְּבָנָה וְדִמּוּ שֶׁהֵאִיר מִזְרָח, וְשָׁחֲטוּ אֶת הַתָּמִיד,

And why was all that necessary? Because once the light of the moon rose and they thought that the east was lit up and slaughtered the continual offering, [and afterwards] they had to take it out to the place of burning.

How could anybody confuse moonlight for sunlight? I've been out in the countryside far from city lights under a bright full moon, and it's nothing like sunlight. (And the moon in this case wouldn't even be full yet.)

The g'mara reports that the school of R' Yishmael taught that it was a cloudy day and light scattered in all directions. I don't buy it; moonlight diffused through heavy clouds looks different from sunlight so diffused.

There's an additional problem: on a full moon, moonrise is the same time as sunset. Moonrise advances about an hour, give or take, per day, so if you count a few days back from the full moon for 10 Tishrei, the moon is rising in the east in mid-afternoon, which is nowhen near the time of the morning offering. By the time it's dark enough to see moonlight, the moon isn't in the eastern sky. Perhaps the mishna meant that they saw the setting moon, except it says "east" and the moon sets in the west.

What confusing lighting conditions is the mishna referring to? According to R' Yishmael, how would a cloudy day contribute to this error?