Yes, this is true but you also have to factor in the marginal propensity to consume, or in plain English, the poorer you are the more of your income you have to spend on necessities like rent or groceries.
There are always high interest investments available to people with a large amounts of spare cash floating about even when inflation is low.
If your rent + utilities + food = your income then you ain't hoarding money even in a deflationary spiral.
This is because inflation isn't a bug it's a feature.
Anything that transfers wealth up the chain, from working class to middle class and from middle class to upper class, is a feature of the western economic system.
For example, in England and Wales the Bank of England is charged with keeping inflation at a target of around two per cent. This means that the pound in a workers pocket is supposed to devalue. The advantage is that the government borrows money in its own currency so inflation means that its debt goes down (in real terms) when inflation goes up.