No, the binlog format is actually irrelevant here; the post author was just incorrect about that part. ALTER TABLE always gets replicated as a statement, regardless of the binlog format.

Auto_increment only has broken replication semantics in the very specific situation the author encountered: a table has data, but no primary key (and also no alternative unique index which could serve as the clustered index key) and then an attempt is made to alter the table to add an auto_increment primary key.

Basically that form of ALTER TABLE statement is telling the database to add a sequential ID to each existing row, but without providing any deterministic way that those numbers should be assigned. So each replica may choose a different numbering, causing the problem experienced by the author.

It's a foot gun, but not a common one in production at any real scale where you'd have a replica in the first place. InnoDB tables really should always have primary keys, and there are various ways to ensure that happens (sql_require_primary_key option, generated invisible primary key option, external linters, etc).