Yes, true, though I think the "Big Four" era was an oscillation....if it started with Andy joining the fray in 2008, 2008-10 was still Fedal with Rafa taking the lead, and Novak and Andy a bit behind, especially in 09-10. In 2011 it was Novak jumping ahead with Rafa next, then "Fedray." 2012 was the most balanced year of the Big Four, all four winning a Slam but Novak being first among near equals. 2013 was Rafa regaining the throne with Novak next, then Fedray a bit behind. 2014 was Novak returning to first among equals, with Fedal behind, and then Murray slipping back. 2015 was Novak's year, with Roger and Andy a lap or two behind. 2016 was Djoray, 2017 was Fedal redux and Andy falling away...
If 2008-16 was the Big Four Era, here are the top 10 players by GOAT points during that period of time:
514 Djokovic
383 Nadal
323 Federer
268 Murray
85 Ferrer
83 Wawrinka
77 Del Potro
68 Berdych
59 Tsonga
54 Nishikori
GOAT points are imperfect, but they illustrate the point: There was a much bigger gap between Andy and the pack, than the Bigger Three and Andy...during the time he was in his prime. The gap becomes larger when we look at their whole careers. But from 2008-16, Andy most definitely was part of a "Big Four," of which Novak was the clear leader. Notice that the gap between Nadal and Federer and Federer and Murray is about the same.