I understand your reasoning, and you're correct in this case (assuming your numeraire is USD). However, if your numeraire is something like a GDP-weighted basket of USD, EUR, JPY, and CNH, it's possible for a USD-pegged asset to be less volatile than USD (since your unit of account isn't USD).
Presumably, your USD-pegged asset would drop in relation to the USD in a risk-off scenario and rise in a risk-on scenario, so in that case it would seem that your tracking error would tend to be correlated to the non-USD components of your numeraire basket. So, if macro risk-on/risk-off are the primary drivers of your pegged asset's tracking error, it would seem that your pegged asset would tend to have less volatility than USD if a GDP-weighted basket of major currencies is your unit of account.