That's mostly true, but I do think captain decision-making matters.
A pivotal turning point in the 2012 Ryder Cup came after the Saturday morning matches. With the Euros down 8-4, Olazabal decided to bench McDowell (who was playing poorly) and pair McIlroy with Poulter. Up until that point, I believe McIlroy had only played with McDowell in his Ryder cup career.
Meanwhile, Love stuck to his strategy of giving each team a rest and sat Mickelson/Bradley, who were on fire. At the very least, Love should have benched Stricker (who was playing worse than McDowell), sat Mickelson, and let Bradley play with Tiger (who played awesome on Friday and Saturday afternoon).
We all know what happened next. McIlroy and Poulter birdied the last six holes to comeback and beat Dufner and Z Johnson. Meanwhile, with no help from Stricker, Tiger almost single-handedly pulled out a halve against Garcia and Donald, but came up short.
Obviously there were 100 other factors that went into the Europe comeback, that that was an area where the captains made a difference.