Sometimes they can be tough to get apart..... but, in my experience, they all come apart. That said - I have not used a spiedel though.
That spigot is suspect #1 for any kind of infection if you have not been taking it apart. I would find a way to get it apart.... maybe even get a new one that definitely does come apart for cleaning after every use.
I have used bottling buckets a lot for fermenters with great success -but, always careful to keep that spigot clean and I always cover spigots with plastic sandwich baggie during fermentation and then spray out with star san before any transfers.