Today, knowing I'd be in a place with less-than-excellent connectivity, I came prepared. I brought two MikroTik 4G routers with me (one, an old friend; the other, new and ready to be tested). I also have my smartphone with two SIM cards from two different mobile providers.
I noticed something extremely curious: the fixed FTTC connection sometimes has extremely strong drops or speed reductions (from 100 mbit/sec to 1 or 2). Knowing this, I brought the 4G routers on purpose to compensate. But I realized that when the FTTC connection fails, all four mobile providers also fail. The phenomenon is therefore correlated. This leads me to believe that, not being in a big city, there is a single (or multiple, but malfunctioning) point of connection that all providers, both fixed and mobile, connect to.
Note for the future: don't trust the mobile providers here.