It's very difficult (if not impossible) to find a way to get the backgound color of a button when it's pressed, because it depends on the style, and it's not guaranteed that the style respects the palette.
However I suggest two different approaches:
You can set you own background color using style sheets (simpler) or implement the painting of the button yourself, using styles or reimplementing paintEvent(). See Customizing QPushButton
To paint over the button with the inverse color, you can set a composition mode to the painter in order to get the inverse color.
For example:
painter.setPen(QColor(255, 255, 255));
painter.setCompositionMode(QPainter::RasterOp_SourceAndNotDestination);
(note that using this example, the inverse color of middle grey (128, 128, 128) is exactly the same color)
See QPainter::CompositionMode