"Is there any actual analysis to support the claim that it is an order of magnitude more complex than AWS crypto or Tarsnap?"

I don't think so, and I personally disagree with this statement.

As a developer, I find bitcoin 0.1.0's code easy to read and understand (I had requested a tarball of it about 2 years ago from one of the developers, as it was not in source control). And even the number of lines of code is not particularly impressive. Version 0.1.0 has only 13k lines of C++ code (excluding GUI code):

     7 ./irc.h
    71 ./headers.h
   156 ./key.h
   177 ./sha.h
   182 ./market.h
   201 ./base58.h
   264 ./market.cpp
   265 ./irc.cpp
   373 ./util.cpp
   399 ./util.h
   420 ./db.h
   498 ./bignum.h
   554 ./sha.cpp
   597 ./script.h
   604 ./db.cpp
   750 ./uint256.h
   856 ./net.h
  1020 ./net.cpp
  1127 ./script.cpp
  1151 ./serialize.h
  1317 ./main.h
  2660 ./main.cpp
 13649 total

Plus 6k lines of (boilerplate) GUI code:

   417 ./ui.h
   720 ./uibase.h
  1806 ./uibase.cpp
  3228 ./ui.cpp
  6171 total

For comparison, many HN readers who are talented developers would consider 5k LoC of C++ relatively easy to write in a span of 3-5 weeks, as a day job, for a small project that they have a precise idea how to implement. So 13k lines for a project that apparently spanned a few months of Satoshi's time is absolutely plausible.

I believe Bitcoin was written by one man.

Source: http://www.zorinaq.com/pub/bitcoin-0.1.0.tgz