Thanks to everyone for their help and suggestions. I went ahead and hacked the spout, and lo and behold! It was held by a sharkbite!! I removed it with a sharkbite removal tool (available for around $2 in Home Depot), and installed the new spout. The thing that was really irritating me, the leak, has now stopped. One suggestion to anyone who might have to do this - using a hacksaw alone isn't enough. You will need a good pair of cutting pliers in order to cut away and remove the hacked part of the spout in order to access the pipe. It took a little effort, but I was able to do it.
For those who are thinking about it, please don't install a sharkbite for the diverter spout, unless you wish to transform a 2 minute job to an hour of tricky work. There are a lot better ways to keep yourself busy!