Pronunciation of thyme

My wife and I have been recently to the United States. Since she is allergic to oregano and thyme, whenever we went to a restaurant, we had to make sure the dish she had picked contained neither of these ingredients. Both my wife and I pronounced thyme with a th sound (as in think), but I noticed all of the locals we spoke to said it like time. I thought that was odd, but I didn't make any comment. I have just done a little bit of research now and have found out that both pronunciations are acceptable, but the time one seems to be more widespread and given prominence in the overwhelming majority of dictionaries. There's even one dictionary that says thyme with a th sound is spelling pronunciation.