We need to be careful what we are talking about here.
Inflation on a economy-level scale at an expected rate will not change consumer habits because the price increase is manageable. You have to realize that prices are not increasing in isolation: wages will have to rise along too.
High inflation that is expected will increase consumption of durable goods, as people attempt to 'get rid of their money' before the price changes on them. A good example of this was post-WWI germany, where hyperinflation was so bad that offices began to pay their employees twice daily, so they could adjust their wages, and so that their employees could go out during lunch and after work to buy something with the money before the price changed on them.
Unexpected inflation may cause a temporary dip in spending until wages adjust, however consumers still need to buy, so they will likely push for higher wages, leading to consumption to stay about level.
There is another effect to inflation as well: People who have savings will have their savings eroded over time if the economy is inflationary. To preserve their wealth, they will invest it. In a deflationary environment, money will increase in value simply by being hoarded, so they will be less willing to invest it. Deflation also increases the cost of interest on a loan, while inflation decreases it. So the overall effect is for an increase in spending under inflation, and a decrease under deflation.
The person you have quoted is quite wrong. Price increases in a particular sector will cause consumer spending to decrease but this is a bad example, as it is not inflation, but rather a supply/demand problem of a particular consumer good. They are applying a micro-economic model (price increases of a single good) to a macroeconomic problem (price increases in the entire economy) when price increases at a global scale have the opposite effects.
A good theoretical test of this is: what would happen if everyone in the US suddenly had twice as much money? (Ignoring international trade, of course).
The answer: prices will double, and nothing else will change.
The reason is, people will have more money to spend, but will require more money for their services, so in the end it all cancels out.