Japanese history isn't my specialty, but yes this was a policy of the Japanese government at one point. It's important to understand that the relationship between the Yakuza, the public, and the state has always been very nuanced. The Yakuza are undoubtedly criminals. However, up until relatively recently, the Yakuza were very out-and-proud, they didn't feel the need to hide themselves like syndicates of their kind usually do.
Of course, Keep in mind that there's no singular organization called Yakuza, what we consider the Yakuza are a variety of syndicates, the most prominent being the Yamaguchi-gumi, but other syndicates such as the Sumiyoshi-kai, Inagawa-kai, and Aizukotetsu-kai are also significant. Their policies tend to differ, for example, the the Yamaguchi-gumi, refuse to deal in drug trafficking.
The Yakuza have been a part of Japan for centuries, and even today they form a big part of their economy and culture. They have fan magazines, they're political lobbyists, there have even been occasions where Yakuza have openly helped the public for nothing more than the publicity. Many people associate them with traditionalism, folk tales, and romanticism due to their history, perceived honor, and the part they played in feudal Japan.
They have a past of working with those in power, particularly the right-wing. One can obviously see the allure of having the Yakuza do the dirty work that is dealing with striking workers. It should be noted that the Yakuza tried to negotiate with the workers rather than resort to violence right away. It should also be noted that they had no problem using violence if they felt like it was the best option. However, this trend has been changing.
In the 90s, Japan passed an act that cracked down on racketeering activity known as the, "Act for Prevention of Unlawful Activities by Criminal Gang Members." There have also been measures put in place to refer to them in mass media as bōryokudan (violent groups) rather than ninkyō dantai (chivalrous groups). For the Yakuza, maintaining their image has been very important to allowing them to operate openly and easily. That's actually been changing in the past 20 years or so, especially with the international community beginning to crack down on organized crime as well.
#Sources
Kaplan, David; Dubro, Alec (2004), Yakuza: Japan's Criminal Underworld, ISBN 0520274903
Sterling, Claire. (1994). Thieves' World Simon & Schuster ISBN 0-671-74997-8
Seymour, Christopher. (1996). Yakuza Diary Atlantic Monthly Press, ISBN 0-87113-604-X