+1/+1 counters are counters. They are, per CR 122.1, specifically added to the permanent or player:

122.1. A counter is a marker placed on an object or player that modifies its characteristics and/or interacts with a rule, ability, or effect. Counters are not objects and have no characteristics. Notably, a counter is not a token, and a token is not a counter. Counters with the same name or description are interchangeable.

Creatures that are */* don't have counters on them by default. This means for example that their power and toughness are not affected by proliferate, Vampire Hexmage, and yes, an effect that says any +1/+1 counters on your opponent's creatures are halved and rounded down. So your interpretation is correct.

The edge case is for a creature like Walking Ballista, which has 0/0 stats but also enters the battlefield with +1/+1 counters. In this case proliferate, Vampire Hexmage, etc, can affect it. Still, Walking Ballista is not a */* creature; it is fundamentally different.

+1/+1 counters are counters. They are, per CR 122.1, specifically added to the permanent or player:

122.1. A counter is a marker placed on an object or player that modifies its characteristics and/or interacts with a rule, ability, or effect. Counters are not objects and have no characteristics. Notably, a counter is not a token, and a token is not a counter. Counters with the same name or description are interchangeable.

Creatures that are */* don't have counters on them by default. This means for example that their power and toughness are not affected by proliferate, Vampire Hexmage, nor the effect that says any +1/+1 counters on your opponent's creatures are halved and rounded down. So your interpretation is correct.

The edge case is for a creature like Walking Ballista, which has 0/0 stats but also enters the battlefield with +1/+1 counters. In this case proliferate, Vampire Hexmage, etc, can affect it. Still, Walking Ballista is not a */* creature; it is fundamentally different.

+1/+1 counters are counters. They are, per CR 122.1, specifically added to the permanent or player:

122.1. A counter is a marker placed on an object or player that modifies its characteristics and/or interacts with a rule, ability, or effect. Counters are not objects and have no characteristics. Notably, a counter is not a token, and a token is not a counter. Counters with the same name or description are interchangeable.

Creatures that are */* don't have counters on them. This means for example that their power and toughness are not affected by proliferate, Vampire Hexmage, and yes, an effect that says any +1/+1 counters on your opponent's creatures are halved and rounded down. So your interpretation is correct.

The edge case is for a creature like Walking Ballista, which has 0/0 stats but also enters the battlefield with +1/+1 counters. In this case proliferate, Vampire Hexmage, etc, can affect it. Still, Walking Ballista is not a */* creature; it is fundamentally different.

+1/+1 counters are counters. They are, per CR 122.1, specifically added to the permanent or player:

122.1. A counter is a marker placed on an object or player that modifies its characteristics and/or interacts with a rule, ability, or effect. Counters are not objects and have no characteristics. Notably, a counter is not a token, and a token is not a counter. Counters with the same name or description are interchangeable.

Creatures that are */* don't have counters on them by default. This means for example that their power and toughness are not affected by proliferate, Vampire Hexmage, and yes, an effect that says any +1/+1 counters on your opponent's creatures are halved and rounded down. So your interpretation is correct.

The edge case is for a creature like Walking Ballista, which has 0/0 stats but also enters the battlefield with +1/+1 counters. In this case proliferate, Vampire Hexmage, etc, can affect it. Still, Walking Ballista is not a */* creature; it is fundamentally different.