Even though the fluid in pulmonary edema is a transudate, there is blood in it. This is substantiated by the fact that there are microhemorrhages in acute lung congestion and hemosiderin laden macrophages or 'heart failure cells' in long standing pulmonary congestion on histology. These signify that RBCs have escaped the vasculature to enter the tissue (and failed to get back to the blood), while the macrophages have consumed them later on.
Since the blood loss isn't very high, the color is pink rather than red as seen in hemoptysis.
The reason for this is likely due to the significant differences in hydrostatic and oncotic pressures when compared with the rest of the body. In the Lung, one edge of the capillary is up against a single, extremely thin alveolar cell that provides very little pressure to counterbalance the increased forces present in pulmonary edema. Without this inward pressure to stabilize the capillary wall, you end up with a situation in which small ruptures occur at weak points in the AC membrane, unlike elsewhere in the body where pressures are more equalized and change is an osmotic process rather than one of cellular disruption.
Although hemosiderin laden macrophages can be a proof that RBCs leave the vasculature, it is important to note that they can be found in other organs too. One example is the chronic venous congestion of the liver, where the hypoxia (due to congestion) can lead to endothelial damage letting out the RBC, which later get engulfed by macrophages.