Thanks for your response Paul. I'm beginning to get the idea that this may be exactly what is going on. I'm still not 100% certain that it's not coming down from above (perhaps a problem with the flashing around the chimney).
To help me decide, I had this idea (perhaps a daft idea), of placing some food coloring in the water that appears to be ponding around the fireplace. If the food coloring shows up inside the house, then I know where it came from. If it doesn't then I just have to take my best guess. Of course, I have the carpet up so the coloring won't damage it if it does get in.