Fireside hosts your MP3 files (your Podcast), creates your RSS Feed (which is how you distribute your Podcast to places like Apple Podcasts, Stitcher, Spotify, etc.), and provides you with a beautiful website.
You do not need any other hosting platforms to host or distribute your podcast. In fact, the only other tools you need to publish your Podcast are the tools you use to record and edit it. Fireside does the rest.
Monetization and membership platforms like Patreon and Supporting Cast work perfectly along side Fireside. Dynamic ad insertion services like Podbean, Soundwise, etc. work independently from Fireside, and may provide their own file hosting separately.