Because Belisario is foreign, and even more so because he already had trouble with the INS and getting a visa due to his DUI infraction, it may be that substance abuse treatment, and thus admitting to it, is riskier for him than for others. While everyone else can apparently go on the DL and be paid his salary, it may be that Belisario (and his agent, and the team) are trying to keep it quiet and unadmitted to avoid problems with the INS, which does not exactly have the highest standards of proof as needed by the courts. If indeed it;‘s a substance abuse problem, suppose it’s not alcohol but some drug that is illegal to possess. While others, even celebrities, seem to be able to avoid prosecution and just have it treated as the illness it is, it could be that merely being charged or apprehended could be enough for the INS to withdraw a visa and deport him. And even if it is alcohol, it may be that terms of his visa or simply having come to the attention of the INS after his DUI last year, might make him, by admitting to alcoholism needing treatment, liable to come under some sort black mark with the INS and even get deported. That could be why they are trying to keep it private, not admit, just deal with it, and forego the salary that comes with admission and being placed on the DL.

All speculation, but not all that unlikely.