Who maintains your AWS instances? You still need someone to create AMIs, script updates, destroy stuck machines, etc. The physical cost of maintenance is pretty minimal unless you have a massive deployment or you have really poor hardware. Especially since if you have a few racks at any decent datacenter they will provide basic remote hands support to do things like replace failed drives.
It is the most ridiculous article I have ever read because it doesn't consider the cost of maintaining and support.
The article does consider those costs:
Note that while labor costs are included in the model, I am leaving them out of this example for simplicity. Because labor is a mostly fixed cost for each alternative, it will tend not to impact the relative comparison of the two alternatives. Rather, it will impact where the actual break-even point lies.
and furthermore, those costs would not significantly differ between the two options, or the other option of leasing servers or VPS instances. You're always going to need sysadmins to organise deployment, maintenance, dbs, backup, etc. even if you use AWS, and in addition you have to deal with all the different AWS APIs as well in order to use their services like glacier, and tailor your app to depend on them.
But price is probably the least important reason to choose your hosting solution; AWS, VPS, leased servers and your own servers have very different properties and levels of control - different companies will have very different load patterns and requirements on CPU, IO, storage, bandwidth etc. Price is just one factor in the calculation.
And how many of those are significantly different between the two options? Either way, you still need one or more sysadmins, you still need a backup setup. Sure, there are extra maintenance costs associated with owning the hardware, but what portion of maintaining a server infrastructure is tied up specifically in that, and how does it scale relative to the size of the cluster?
In my experience of managing a team of 10+ admins, less than 5% of their time was spent dealing with physical hardware and that includes installation and repair.