You are oversimplifying it.
I don't think so.
In any situation in neutral, both players
can't wait for their opponent to act; the onus is on one of the two to act first and expose himself to risk. Sometimes this is matchup-dependent, sometimes percent-dependent, but someone must eventually do something that could lead to either of the two taking damage.
Let's take the example of two Ganons dancing around each other in neutral on a flat stage. They're simply initial dashing and waiting to shield in the event of a Wizard's Kick, without moving far enough forward to be hit or get into each other's grab range. Ganon's dash grab is pretty slow, and Wizard Kick is reactable from any safe distance, so there's very little risk here; neither player will ever take damage. This is a defensive stalemate. When does this stalemate end? When one of the Ganons takes some kind of
risk. If one of them runs forward and stands within the other's grabrange, the stalemate ends, at the cost of which the Ganon player who acted first left himself open to getting hit.
The initiator is then the one who first exposes himself to risk. This risk is the foundation of aggressive play.
Meanwhile, setting up a situation which enables you to react to your opponent's initiation with limited risk is the foundation of
defensive play. Sometimes, this can look like an offensive option. Cloud spacing an immaculate up-air on your shield in Doubles with a teammate at his back can look very offensive, but it isn't necessarily--because what is the functional difference between (completely) safe shield pressure and shielding? Offense without any risk may as well not be offense. We don't call juggling a falling Captain Falcon with Mario an offensive play, because there's so little risk involved that you'd be silly not to juggle him.
Now note that I did use the word "limited" here. Obviously aggressive vs. defensive isn't a binary; options and sequences can sit somewhere in between, such as when an action is mostly but not completely safe. In this particular game, no option is completely safe. But there are two very obviously different styles of neutral gameplay. There's the mixups and read-based type of gameplay exemplified by Ally and ESAM, and the heavily reaction/positioning-based type of gameplay exemplified by Salem and MKLeo. Our #1 for years has been ZeRo, a player who mixes up both styles effectively. He uses a blend of offense and defense to win, so the two need not be mutually exclusive.
If I initiate a perfect pivot back and my opponent rushes in to attack, is that an aggressive play on my part? Of course not.
In this case you aren't initiating any kind of interaction, you're setting up for a future interaction. Perfect pivoting backwards, as well as things like SHAD, are intuitively understood to be defensive options, because of the risk involved. The opponent "rushing in to attack" is the risky play. Not your perfect pivot backwards.
What matters about your definitions has to do with what the players are initiating. If I initiate a series of attacks on my opponents shield to pressure them into making a more limited, but predictable decision, that is me being aggressive. I am attempting to limit their options with my attacks. Pressuring is pretty basic offensive play out of neutral.
Just because you are throwing out a hitbox doesn't mean that your play is aggressive, and limiting your opponent's (safe) options is exactly what defensive play is all about.
Not limiting your opponent's options in any way is just bad defensive play.
Kirihara dash attacking Clouds in neutral is aggressive.
Dabuz spacing around Elegant's shield with a Luma jab is not.