True, but not in the way of Pep, but more of Dutch school. I don't think it started from 2004 but after EURO 2008. I'll explain
Low & Klinsmann started from 2004 (after failed EURO. Taking shape in WC 2006) with the new Germany wave of more technical oriented players. They're less rigid, or static than the old typical German football. It's more expansive & attacking oriented, but not possession football. It's similar to England when they're a force & a transition team than a possession based. They used actual wingers, one central forward with a second forward, 2 holding midfielders... the second forward was allowed freedom & less defensive duty to support the main forward.
EURO 2008 they approached the game more conservatively. Instead of midfield 2 with a second forward, they changed to midfield 3. The midfield dynamic is similar we see teams often use around this time. 1 midfielder sit before the defense line & 2 midfielders work both defensively & offensively. No real no 10. The 2 winger are more wing forwards as they're allowed to move inside (off ball) more from wide position. They lost the final to Spain.
Between EURO 2008 & World Cup 2010, Barcelona dominated & LVG happened to come to Bayern & shaped the structure for possession football. Come World Cup 2010, Germany changed alot. They're now defending in numbers, slower build up so they can attack in numbers (total football principle). To achieve that you natural need to work on positional play to learn to keep & pass the ball better. Even forwards were asked to take part in defensive shape & building up. The exchanging role which you see in total football, defender step up becoming midfield with midfield step in to take the position. Midfielder move to wing with wide players move into midfield... It all started here.
Low tweaked & improved over the years based on Bayern system (the most balanced one is during Heynckes year where he find the balance between possession & direct football German players suited), but arguably they're more Dutch than Spanish, Pepism

as simply the nature of German players are different than the Latin counter part that Cruyff philosophy built toward. Pep is a student of Cruyff. He learnt from LVG who is the pioneer of (ultra) possession football (he improved upon the total football adding his pragmatic approach to boost possession stat). Pep adding idea from Bielsa who is pioneer in congest & suffocate opponent in their own half with their pressing. This is helpful to prevent back to back football game which favor athletic team (usually from Europe). Pep did bring his idea to Germany & they (Low, the other German coaches) exchanged with his idea. However, as it proved the Germany based on Dutch football had more influenced on Pep than the other way. Pep had to adapted his way more toward more direct football toward the end of his time at Bayern.
Edit: One of the main flaw/ weakness of Pepism that is the use of no 9. He prefers a mobile modern forward who has play making ability & working outside the box alot. He didn't fancy Muller or Lewandolski that much. That may be what Germany wants to learn from him since they haven't produced a good old school no 9, but second forward. You know Low still called Podolski up at times. He was forced to try Gotze as false no 9.