"Is `data` a singular or plural entity?" is a question you should ask yourself.
In this case their data is a collection or mass of data - and is singular. In the blog, using "the data shows that" is the proper way to write the statement.
This may be a British/American English gaffe. Collective nouns in British English are referred to using plurals, e.g. "Apple are planning a new product," vs. the American "Apple is planning a new product."
Perhaps. I know it as a more modern linguistic split that isn't really related to the British/American divide. Regardless of the reason, many linguists would laugh someone like them out of the building. Living languages are constantly changing and while somewhat steady rules ensure there is less confusion - the majority will always win.
If the majority of people refer to collective nouns as singular than that is the correct way to use them because the "correct way" is only ever defined by the majority.
How is the pronunciation of a word decided? Majority of people saying it one way. How do people agree upon the meaning of a word? Majority of people using it to mean something. How does grammar become more lax? Majority of people speak with fewer restrictions.
i contest the moderne way of speech is to be thovght proper as he has argvede, bvt the olde way of speeking is the trve way!
In this case their data is a collection or mass of data - and is singular. In the blog, using "the data shows that" is the proper way to write the statement.