The water might not be de-ionized, but it's probably distilled. To make it to the dehumidifier's water receptacle, it must be coming from humid air. In that case it is in the form of water vapour. The dehumidifier condenses it from the air into water in the dehumidifier, hence it is essentially the same as distilled water. This is pure water and should be excellent for your radiator. De-ionized water is another way of making "pure" water. Instead of boiling and recondensing water (distillation) to leave the impurities behind, de-ionized water is made by passing the water through an ion exchange column which removes the unfavourable ions like salts and metals and things. I think your friend is right to use the water from his humidifier in his car because it is distilled water.
While distilled water from the humidifier would be excellent used as make-up water for a car's battery, it might not be the best thing for the cooling system. Impure water such as tap water or water with antifreeze boils at higher than 100°C, and freezes at lower than 0°C, both desirable features for a radiator. Distilled water is also more likely to dissolve pipes & protective pipe linings in your automobile's cooling system.
Although water from a dehumidifier is condensed from the air, it is only as clean and pure as the air space you are dehumidifing. House air is not very clean. Just look at your furnace filter. If you have pets or if you heat with wood, the air can be very dirty. The "dirty" air passes over the wet coil in the dehumidifer and particles "cling" to the water and drip into the tank with the water. It varies from house to house. By no means could you call this distilled water but it might be much better than tap water for mineral content depending where you live and what particles are in your air.
This is from observation only, no tests or experimental evidence to back this up, so I do not have any idea of relationships of particle size, how many particles are present, material typek, or coil design may effect how dirty the water is. Over the years I have designed, installed, and serviced many dehumidifier systems and whatever is in the air will end up in the condensate drain, often blocking it, oversized piping helps, or special lint or fibre traps. For instance, with pool systems if the water chemistry gets out of control--common with residental pools--then corrosion of the dehumidifier coil, drain pan and piping can accelerate. I always assumed that the corrosive chlorine or bromine compounds carried with the water vapour from the pool did this when condensed on the coil.