I would have serious doubts that bitstamp even runs one single full node of their own ... probably outsourced.
you *seriously* beleive that a major bitcoin exchange does not operate thier own node? Something that can be achieved for <$100 with a standalone device and uses <64GB of storage?
get real. you can buy a 1TB harddrive for $50 today and store BIP101-enabled blockchain onto it for years to come. then pay $50 more for a 4TB drive to handle a few more years of growth. or are you still using the same computer you owned in 1999 with its 1.6GHz singlecore, 512MB ram, and 60GB HDD (all cutting edge)?
Running Bitcoin core is another thing than building a complete software stack for an exchange.
There's a reason companies like Chain, BlockCypher, etc. exist. I wouldn't be surprised to know that Bitstamp uses one of these companies API to support their operations. Hell they run BitGo's multi-sig wallet code. All that jazz strapped onto Bitcoinica footprints. What could go wrong heh
Mike Hearn has often hinted to this himself. There is important developer's cost into building a full fledged node software. Specialization in that regard is a real concern.