Radar relies on electromagnetic wave propagation: from a source, to the target and back to a receiver.
Anything that alters the behavior of these waves along the way will impact the performance of the radar station. For example:
- A target hiding behind terrain will be harder (but not necessarily impossible) to detect, because the terrain will absorb the outgoing emissions before they even reach the target.
- If the target is in plain sight but shaped in such a way that all the incoming radar energy is reflected in a direction different from that of the receiver, then it will not be detected (this is the method employed on the F-117).
- If the target is in plain sight but the return signal comes back accompanied by a lot of duplicates purposefully emitted by the target, it will complicate the task of figuring out which is the correct reflection, delaying or preventing a valid solution.
- If the target is coated in a material that absorbs all the incoming energy, the radar station will never see a return, and thus think there is nothing there to detect (another technique used by Low Observability aircraft). This one is relevant to your question!
The media between the emitter and the target needs to allow the waves to travel, and while the best media is vacuum, air is not terrible either. At least normal, ISA air, things get complicated in the high atmosphere, or at high temperatures, or when electromagnetic fields (caused by thunderstorms, the Earth's core, etc.) come into play.
In the case of water suspended in the atmosphere, it can absorb the radar emissions and thus limit their effective range. However, it does so mostly at certain wavelengths, which are the ones at which water molecules can best capture incoming energy. One such wavelength is the one used in microwave ovens, because food tends to contain water, and heating the water is a fast way of heating the food.
So the ultimate answer to your question is, there is some kernel of truth in those statements, but how large it is is very debatable. Some radars, particularly modern high-frequency ones, operating in the millimetre band, will see noticeable losses due to coulds. Other radars, particularly those in the low GHz range or lower, will fare considerably better, although the lower frequencies have their own disadvantages in terms of resolution and antenna size requirements. Ultimately, defense organizations are quite aware of their equipment's capabilities and usually take steps to mitigate any drawbacks, so it is unlikely that some cloud cover will substantially impair a modern IAD network.
