Several commenters are joking about how many times they've heard this before, but NASA goes into great detail about why it was so difficult to measure and what new information helped them decide for sure. Here's a small excerpt:

"The particular oscillations meant the spacecraft was bathed in plasma more than 40 times denser than what they had encountered in the outer layer of the heliosphere. Density of this sort is to be expected in interstellar space."

Read their account of how an "unexpected gift from the sun" helped them. It's not long and quite fascinating, and some little tidbits like this are pretty intriguing to me:

"By the time the signals get to Earth, they are a fraction of a billion-billionth of a watt."