Well, one of the main tools for data analysis, R, is already free ("democratized"). That said, automated access to datasets, natural language parsing and other AI goodies lower the barrier to entry for non-professionals.
If you had to pay $4.99 to vote I suspect people might complain about how "democratic" that was. It's at worst a bit of an over-reaching use of the word, and not some horrible evil conspiracy to exclude poor children from doing maths on the interwebs.
You do pay a lot more than $5 to vote in the form of taxes. If you stop paying your taxes, will you still have your right to vote after your sorry ass lands in jail for defrauding the IRS?
I love Wolfram|Alpha but I don't use it all the time. In fact sometimes I go months without using it. I'd love to see some other sort of payment schedule... Like free suscription and a modest charge per query & data transfer.
The term is here being used to indicate that it is increasing access to something that has previously been limited to far fewer people. It does not need to make it available to everyone to still be vastly more accessible than before.