Bit of both. From Wikipedia:
Winners Don't Use Drugs is the name of an anti-drug slogan that was included on all arcade games imported into the US from 1989 through to the year of 2000. The message appeared during the attract modes of both video games and on some pinball machines. It was established by FBI Director William S. Sessions with an agreement with the American Amusement Machine Association.
It was part of the government's Just Say No campaign, and, by extension, part of the larger War on Drugs effort. By law it had to be included on all imported arcade games and continued to appear long after Sessions left office. The quote normally appeared in gold against a blue or black background between the FBI seal and Sessions' name. Sessions' name was removed from this background in games released after 1993 as he left the bureau and was, in effect, no longer affiliated with the program. Earlier games used a blue background, while later games utilized a black background.
His name was often concatenated into "Williams Sessions" by many non-English-speaking, primarily Japanese, game companies
I can't remember the game but there was at least one beat em up that features bush (or a generic bushlike president) at the end of a level parroting the winners don't do drugs slogan