In the previous few years Liverpool had been very successful by concentrating on possession to the point of working the ball up from the backs rather than hoofing the ball up with a big goalkeeper kick. They were a clear counter-example to this admonition that the way to win was hoof it and chase.
Sounds like "horses for courses" to me [the correct advice varies according to the characteristics of the situation].
Not really up on Football (soccer) but this reminds me of the puck possession vs dump and chase zone entry debate from hockey.
For a lot of reasons (up to and including global geo-politics) North American teams for a long, long time over-emphasized dump and chase The basic tactic is that you carry or pass the puck up until it will no longer cause an icing call then throw it into the other teams defensive corner and send your forwards in to generate a turn over.
Until reasonable statistical analysis this was thought of as the "right" way to play the game. Actually it was long AFTER the statistics showed it because politics was playing a role in what the statisticians wanted to find. They wanted to prove that the NA way of playing was "right" so they went and found stats to prove it. It wasn't until a combination of the NHL rising ascendant, the fall of the Soviet Union and I would argue the fact that Canada missed Gold in the '92, '94, and '98 Winter Olympics that forced Hockey Canada to look at their developmental programs and do some honest analysis.
Today though, much like in this article short quick passes and maintaining possession through zone entry is preferred and the statistics back that up. I'd imagine that if what you say Liverpool has been doing it true it's for similar reasons, maintaining possession allows you to generate more shots, shots are important if you want to score, ergo keeping possession is important for scoring.
Sounds like "horses for courses" to me [the correct advice varies according to the characteristics of the situation].