What you are talking about is the difference between True Airspeed (TAS) and Indicated Airspeed (IAS). IAS is what is shown on the pilot's Airspeed Indicator, and is important for the aerodynamic handling of the aircraft, but at high altitude it is significantly lower than the TAS. If you like, IAS is the number of cookies per second, but is less than the actual speed. TAS is used for navigation, and is the maximum speed quoted by the manufacturer.
What this means in practice is that the aircraft is faster at altitude, as you suggest, but this is already the limiting speed quoted by the manufacturer. If the limiting TAS is, say 500 knots, the pilot might reach this speed when he sees only around 300 kts on the Airspeed Indicator.
Its not that the aircraft is exceeding this limiting speed at high altitude (low air density), its just that the pilot is actually seeing a lower figure for IAS. The minimum air density (in other words is maximum altitude) is specified, again, by the manufacturer.
It is quite categorical. The aircraft will not travel through the air, at any density which it is certified, faster than the manufacturer says.