If the Anti-Deficiency Act is not used as justification, then your interpretation of the law, as applied to the web shutdowns, is moot.
If the Anti-Deficiency Act is not used as justification, then your interpretation of the law, as applied to the web shutdowns, is moot.
Here's question 5 from page 14:
Q5: What if the cost of shutting down a website exceeds the cost of maintaining services?
A5: The determination of which services continue during an appropriations lapse is not affected by whether the costs of shutdown exceed the costs of maintaining services.
[1] http://www.whitehouse.gov/sites/default/files/omb/memoranda/...
Well, I found it in the first page of Google results for the citation you provide:
http://energy.gov/sites/prod/files/2013/10/f3/Shutdown.OLC_....
Math is not an issue. The legal issue isn't the quantity of funds that can be spent in the absence of appropriations, but the purpose for which funds can be spent in the absence of appropriations.