The parent is leaving out the demand side of supply and demand for the dollar. If one increases the money supply ceteris paribus then one may expect prices to rise and the value of a currency to fall. However, if foreign investors' expectations of the future performance of the US economy improve, then there will be more demand for the dollar and its value will rise on international currency exchanges. This reduces the price of foreign goods and combats inflation.

In practice, it is possible to engineer a short-term economic boom by increasing the money supply, so the supply and demand of dollars work against each other and it is impossible to say where its value will go. In the long term, the purchasing power of the dollar has dropped constantly since it went off the gold standard. However, nominal income and wealth has increased faster than the dollar's decline, so our living standards have increased.

I'm not an expert, so it's possible I am missing some big factor. However, I do have some training in the field, so I hope I am more right than wrong.