According to one unofficial field test conducted by Super Street Online, brake fluid has little to no effect on car paint in the short term. Prolonged exposure to brake fluid may damage paint, but it generally takes longer than a week of sustained exposure.
Brake fluid does contain chemicals that are potentially corrosive to paint. However, after seven days of consistent exposure to brake fluid, the paint on a test car was not damaged in any way. The test car had been painted using a three-coat system that included priming the car with a base coat and sealing it with a top coat.