Thanks to everyone for their help so far. I am getting closer. Livestreamer worked for me to capture the link given by the first responder. The problem I'm having now is extrapolating this process to the other videos. I used Wireshark to get this address, for instance:
/services/mobile/streaming/index/rendition.m3u8?assetId=4445774836001&pubId=1290862 567001&videoId=4445730444001
Which I added to the
http://c.brightcove.com to get
http://c.brightcove.com/services/mob...=4445730444001
I tried this with the same livestreamer format given above, changing a few things in the address to look more like the original link you provided (I changed rendition to master and removed everything from the & onward) and livestreamer returns a 404 error. I tried the link as it was as well and it said there were no streams found.