ECG is widely used to teach PPG-only models, yet what it teaches is unexamined.
Wearables are valued for tracking how a person's cardiovascular state changes, but ECG-to-PPG distillation mostly learns who the person is.
A per-recording mean, the trait, holds 40-59% of a frozen ECG teacher's target, and pooled students memorise it without carrying it to new recordings.
The raw alignment cosine misses this, since a constant predictor scores 0.793.
Across 34 runs, the more identity a student memorises, the less state it learns.
Fixed-effects distillation subtracts each recording's mean from prediction and target, so the trait cancels exactly, while a pooled anchor keeps it.
State agreement more than doubles, within-person labels improve while age and sex do not, and the gain holds on two backbones and two further databases.
Conditioning on the recording turns distillation toward the within-person changes that wearables monitor.