I would say a little bit of both. Since modern networked programming is much more complex than before (having to care about security, distributed storage, systems, worldwide connectivity over vast range of devices etc.) it has more moving parts and thus more combinations of various systems possible. Naturally complexity grows exponentially.
>...complexity grows exponentially
Just to nitpick a bit, I would say that complexity grows quadratically - proportionally to the number of potential interactions between subcomponents.
Is this because this Web programming innately needs lots of tools, etc. to work, or because the modern programming ecosystem (including stack overflow) has allowed it to grow to be this way?