It's very much the case, so long as you stick to standard C (the full limitations of which very few people are actually aware of).

Runtime backwards compatibility is similarly extensive on platforms that care about it. You can still take a DOS app written in ANSI C89 the year that standard was released, and run it on (32-bit) Windows 10, and it'll work exactly the same. In fact, you can do this with apps all the way back to DOS 1.0.