[Rogach]

Inside a single bank - definitely. But if you have dollars in different banks then they suddenly start having very different value. Couple examples just in case:

1. Spending dollars on US soil from an US bank account won't incur extra fees (at least visible to the person - I know about interchange fees, but they are borne by the merchant), while using card issued by a foreign bank can incur fees for cross-border transactions (at the level of 2-3% usually).

2. Sanctions and KYC concerns also make different dollars have different value. Money in US bank account of an US company employee can be used at face value - money in some less-favored country bank, not so much.

[Eddy_Viscosity2]

This examples don't mean the dollars aren't fungible only that where they are stored can make them less accessible or subject to fees. Its like the difference between a gold nugget in your hand and one that's buried deep in the ground. The gold itself is inter-changeable, one nugget is worth the same as the other if side by side. Only one is in a more inaccessible location and you'd have to pay the cost of retrieving it. If you magically switched the two nuggets, the situation would be exactly the same from a value perspective.