See Air France SA v Heinz-Gerke Folkerts and Luz-Tereza Folkerts, where the European Court of Justice (ECJ) ruled that just because the original flight was not delayed beyond the limits laid down by EU law does not affect the right to compensation. In the case, Mrs Folkerts held a single ticket from Bremen, Germany to Asuncion in Paraguay via Paris and Sao Paulo. There was an initial 2.5 hour delay out of Bremen, that caused her to miss her flight from Paris to Sao Paulo, and her later rebooked flight to Sao Paulo also caused her to miss her original flight from Sao Paulo to Asuncion, resulting in a total 11 hour delay.

Air France argued that since the initial 2.5 hour delay was less than the 3 hour delay required for EU 261/2004 to apply, it wasn't liable for the 600 EUR it had been ordered to pay. The Court of Justice disagreed with Air France, and ruled, bolding mine:

"...a passenger on directly connecting flights must be compensated when he has been delayed at departure for a period below the limits specified in the regulation, but has arrived at his final destination at least three hours later than the scheduled arrival time. That compensation is not conditional upon there having been a delay at departure."

Just note that the entire journey must be on a single ticket; naturally, if Elliot and his family had held a separate ticket from Washington to Orlando there would be no compensation due. And if there was a stopover such that it was no longer part of a single journey, the delay out of Washington wouldn't count either for purposes of EU 261 compensation.