No. The Occupational Safety and Health Administration (OSHA) does not set maximum standards for safety within the workplace. In fact, there is, in legal terms, no such thing as maximum standards for safety.
OSHA does set the standards for safety in the workplace. It does this by drafting proposed rules which are then put out for public comment. After the period for public comment, the proposed standard is either accepted, revised, or rejected. These standards are not maximums, though. Any business is certainly free to make its workplace safer than it is required to be. There is no law that says a workplace must not be made excessively safe.
Therefore, it is more accurate to say that OSHA sets minimum standards for safety, not maximum standards.