You don't have to be a US citizen to purchase property in the country. This is the same for many of the European, Central/South American and South East Asian countries. Is it as straightforward as being a citizen no, but it can usually be done without much extra effort.

Also, given the exit tax, he'll have to pay taxes on them as if he had sold the properties, despite the properties not having been sold.

My reading of the exit tax is it is merely paying all the taxes on any gains that you have made but have yet to pay. For example if you have bought stock but not sold it you would be taxed on the gains you made. This applies to real-estate and other holdings as well.

To me this makes sense it is like you paying your final taxes before leaving as such I don't see how it is anything additional but I could very well be mistaken.

He did not renounce his citizenship, where are you getting this information?