Are basic lands legal in every format by definition?
Basic lands are only legal in a format if they were printed in a set that is legal in that format.
The formats are defined in the Tournament Rules, not the Comprehensive rules, and that is where deck legality for each format is defined, specifically in section 6.
The rules do not explicitly say that basic lands are allowed, rather they say what sets are legal for each format, and what cards are banned. As you mention, every one of Plains, Island, Swamp, Mountain, and Forest have been printed in every set, so they are therefore legal in every format. Any other basic land is only legal if a set in which they were printed is legal.
The Standard deck construction rules in particular say

When Snow-Covered Lands are not legal in Standard, they are treated as the equivalent basic lands. Players must replace them when discovered, but no infraction is committed.