Diablo – Bosses no longer dropping rare

"Dropping your banner" with G is an emote that serves no immediate function.¹

At best, it's a customizable emote that shows off your swag—your in-game achievements convert to banner adornments. You can also change the banner's color, sigil, and shape to reflect your taste.

Dropping the banner will create a marker on the map for party members (orange arrow, turns to pulsing circle when close)

It's true... sort of.

The rare drop rate is substantially higher for first time kills of major bosses on normal mode, but it isn't necessarily two drops guaranteed - the specific bonus and which bosses it applies to hasn't been laid out explicitly. For what confirmation does exist, see this post by Bashlok:

The bonus to drops for first-time boss kills only exists in Normal difficulty.

Whether the 'bonus to drops' is 'guaranteed class-specific yellow', or simply 'twenty percent increase to the chance to drop' is unclear, and without a very large data set or some (very unlikely) additional candor on the matter from Blizzard, it's difficult to say. Anecdotally, people seem to be citing the '2 rares, one for your class' fairly widely, and I'm yet to personally have any experiences that contradict that - at least on major bosses. If I had to guess, I'd wager the Skeleton King doesn't qualify as one however.