The Archangel Network, yeah. It's the same kind of applied phlebotinum as the Barber's "web of life and destiny" (I wonder how many people will get that reference, lol). Literally runs on narrativium!
Which the show always has. Being annoyed at the ultra-soft "science" of the show becoming pure fantasy strikes me as pretty odd. The Doctor is a magician who can wave a (literal) magic wand at problems. Deus ex machina being employed to save the day are as old as the show itself, and the Doctor's explanations are often utter nonsense. "Reversed the polarity of the neutron flow", and so on.
Even when the show establishes rules for it's main conceit, that of time travel, it has no problems ignoring them if it makes the story work. See "Blinovitch Limitation Effect" (which apparently stopped being a thing after the Time War, as per the events of "Father's Day"- just pretend Ace didn't hold her own infant mother that one time), the Doctor's supposed inability to alter fixed moments in time (which happen only when time travel isn't allowed to be the answer- thus Rory and Amy are trapped in the past, but "The Waters of Mars" could totally happen) etc., etc..
Or how people lambasted "bi-regeneration" but seem to have forgotten about Logopolis where Four's unregenerated future self was roaming about, only to merge with him to allow the regeneration into Five- how that's any less silly or nonsensical is unclear to me, but one is considered a classic moment for the series and the other is "ridiculous NuWho terrible writing", lol.
Utterly ridiculous stories are the essence of Doctor Who, I don't know how to express this any better. Whether it's Ten and Donna encountering kung fu werewolves in Elizabethan times or Three disguising himself as a cleaning lady to infiltrate Global Chemicals, there's plenty to roll one's eyes at. Most of the time, I find it part of the show's charm (but even then, there are stories I just can't forgive, like "Time-Flight", "The Twin Dilemma" or (shudder) "Love and Monsters".
Or the infamous TV movie, for that matter, which has more insanity than I really have time for.