Yes the dollar is stronger against the euro than it has been in many years. That trend might get even better, or it might start falling again. There is no way for the average person to know or predict, and even veteran currency traders sometimes get burned. Lesson, don't try and play the currency markets. Get a little cash ahead to have in your pocket on arrival if you want, but get the rest as you need it from ATMs.
The other reason to avoid buying now is that you will most likely pay between 5-10% to buy currency in the US. That comes either or both in fees and poor exchange rates. When getting cash at an ATM, you pay the current interbank rate and any fees charged by your bank (some have a 1-3% foreign transaction fee and some have an out-of-network fee). Some banks don't have any fees using the ATM and it's easy to open an no-fee account (several get mentioned here a lot).
In Ann's example, she claimed to have just bought euro for 1.22. The current interbank rate (which you would get using an ATM) is 1.156. That's about a 5% difference. Not too bad really for buying here in the US, but a far cry from free or just a few percentage points. And it's been steadily dropping, which means any euro bought recently has lost its value.