This is absolutely not true at all. 'Ah' is a measure of capacity and 'amps' is a measure of current. Batteries typically have three measurements: nominal voltage, capacity (Ah or mAh), and rated continuous current (amps).
> watt hour measurements are path dependent
Watt hour is a normalized measurement of the battery's capacity. For example, it lets me compare a 12v/100Ah LifePO4 battery versus a 3.7v/3Ah Li-ion 18650 battery in terms of each batteries capacity (in this case 1200Wh versus 11 Wh).
For example, 1C is rated continuous discharge amps, which means a 1C rated battery will provide 1 * Ah. So if a 20,000 mAh battery is rated for 20,000 mAh @ 1C, it will (in theory) discharge 20,000 mAh at 20A in one hour.
> You can of course estimate the battery capacity in watt hours, but it’s not how the battery is classified (eg in a data sheet)
You're right but this is irrelevant because real life usage highly varies. Data sheets are just guides.
Most lithium batteries can drain themselves much faster than an hour.