Ah you make a point that we have to take into account the stars the sun is physically blocking. If there are at least two stars behind the sun (and whose light is not gravitationally lensed around it), then night is back in the lead.

Everyone's being adequately pedantic about what constitutes a 'sun', but what about what it means to 'see'? Sunlight doesn't block light from stars from reaching our eyes, it just drowns it out. So in the day, our eyes receive light from all the extra-solar stars plus one solar star.