@cin82 Sir, you have gone from "a problem with starting the car on a cold engine" and "it fires worse as it rains" to now: "they gave back the car that worked for them (because it didn't rain)".
If they had kept the car over-night, they would have had a cold start no? You are stating more conditions than I can understand. Bottom line, the car always starts; it's just harder starting when it's cold or it's raining yes? A competent mechanic should be able to troubleshoot that. Have they looked for any diagnostic codes with their OBD2 reader? Is this even a authorized Mazda Service Center you are taking the car to?
I have nothing more to add except that if the car cranks but doesn't start and you un-plug the MAF sensor and it does start then that is the problem. That being said, I have never seen a diesel CX-5 in my life. All of our here in America are petrol engine powered. Good Luck.

 

That's how a car always starts, but when it rains it has a harder start. OBD no show any errors. I've connected it myself, too. That's why the mechanic didn't find any mistakes. Unless the errors are only temporary when it rains, and when I take off normally, they're gone.