Effects of multiple voltage sources in a transformer
You are correct for the case of a perfectly coupled inductor (mutual coupling = 1 with no leakage inductance).  A coupled inductor buck converter will not work if the mutual inductance is ideal.  These converters rely on self inductance or "leakage" inductance of the coils and are wound on cores that have additional flux paths to deliberately lower mutual inductance and increase self inductance.  This makes the analysis more complex.  Try reading the introduction of: https://vtechworks.lib.vt.edu/bitstream/handle/10919/28469/ETD_final_Rev2.pdf?sequence=1