Almost everything he says is inaccurate, but there is a kernel of truth to the story. If he knew what he was talking about, he could have made his point about ancient Athens much more strongly.

First, let's break down what he says:

We're going through a societal economic panic. The Greeks when through this in 700 BC when they invented coins.

The Greeks didn't invent currency (it was probably the Lydians, as the Greeks themselves believed), and it happened nearly 100 years later. The oldest coins ever found date to c.600 BC.

It took them 200 years to figure out what to do.

Hardly. Coinage spread rapidly as an acceptable and practical replacement of older measurements of value, such as oxen or bronze bowls or tripods. They allowed for much greater efficiency in paying large groups of people (such as mercenaries) and for standardisation of measures between different city-states. It simply made existing forms of transaction, trade and wealth accumulation easier. There is no sign that it caused some kind of social crisis. Conflicts between rich and poor had existed beforehand and would continue after.

The Greeks came up with the moral basis of progressive taxation (...) And when they came up with this moral principle, they invented democracy.

These two things are not, in fact, related. The concept that the rich must fund the state is much older than democracy; it is one of the fundamental principles on which all Greek city-states were built. Wealth came with status and privilege, but also with responsibilities to the community. No one ever seems to have questioned this, since the Greeks were well aware that the poor had no money. Even the rich accepted that they would always be the ones who had to pay; what the Greeks argued endlessly over was how much power they should get to wield in return. Democracy arose out of fears that the rich found it too easy to turn their wealth into power.

Now, let's consider that kernel of truth. Yes, the Ancient Athenians had a system of progressive taxation. In fact this term might not be quite radical enough to describe what they had. It wasn't like our modern system of progressively higher tax rates for people with higher incomes. In Ancient Athens, the poor paid no tax. The rich paid all the tax. Your property determined what forms of taxation you were liable to. If you refused to pay, the state would confiscate everything you owned.

This system grew quite naturally out of the sort of society we find in Homer's epics, where wealthy warriors were supposed to distinguish themselves by their ability to defend, counsel and provide for the communities that supported them. As states became more organised, the system of providing for defence became formalised; rich men were made responsible for "districts" that were each supposed to muster, for example, a ship or a number of horsemen. The status that came with being a ship-owner or a heavily armed warrior was matched by social pressure to prove oneself worthy of the privilege, which became simply a matter of conspicuously spending your money on your prescribed public duty. When the community needed money - for instance to build city walls or hire mercenaries - emergency "contributions" were demanded of those who could spare them. It is this system that was eventually (we're talking hundreds of years later) expanded into a regular tax applied only to those above a certain property level.

Presumably, few rich men were very keen on paying such "contributions" and performing their duty to the state. In the 4th century BC we hear of people bankrupted by the duties imposed on them - worst of all the trierarchy, the responsibility to pay for sails and a 200-man crew for a trireme for an entire year. However, it was clearly still an ideal among the leisure class to be known as a shepherd of the community, and to be seen spending money on public needs rather than personal extravagance. One man was accused in court of making other trierarchs look bad by the sheer amount of money he lavished on getting the best crew and tackle for the trireme he had to fund that year. Such spending increased a man's standing and prestige in other ways than the mere accumulation of coin. Xenophon speaks constantly about the glory in being able to help your city with the money you possess:

Those who can maintain their own estate and yet have enough left to adorn the city and relieve their friends may well be thought high and mighty men.

-- Oikonomikos 11.10

'As you want to win honour, is it not obvious that you must benefit your city?'

-- Memorabilia 3.6.3