All fair points. My response was a little harsh and possibly ad hominem. Apologies for the aggression.
In fairness their explanation is not a model of clarity, but the impression I get is that there are legacy concerns here. Perhaps they are using some type of split horizon DNS for access to internal services.
The resources necessary to make this kind of change aren't necessarily raw compute power (which as you point out can be purchased cheaply), more the necessary people and access to investigate the impact that such a change would have, then assuming it's viable, document the change, get signoff, then make the change.
I work for a company that has < 500 employees, but our IT infrastructure (which includes corporate IT and a web site handling a comparatively tiny 3m uniques / month) has a history that can be traced back around 15 years. Changes can be hellish, however small they first seem.
It's also worth bearing in mind that in a large organisation, independent projects (such as the Eyes on the Solar System product) are so much easier to get done than those which require interaction with other departments.
Basically, getting shit done in large organisations is hard. A lot of it is paperwork, which is annoying, but a lot of the paperwork is necessary - in a 5 person startup you can just shout across the room (or drop them a text if they've left the company), but at an organisation with hundreds (or thousands) of employees there must be protocol and documentation in order to competently deal with employee churn and similar.
No idea if I'm right about this, but hopefully it was more constructive :-)