I know that this question has been answered back in 2012. But is the answer still valid as of today - 2019?
This is actually country- and company-dependent.
Some companies will force you to use the miles you get from flights they paid for for future business travel. Most will not. It often depends on the country, as there may be specific regulations one way or the other, or just a “culture”. I think I have read somewhere recently that in Germany for instance this happens quite a bit.
Some view frequent flyer miles as benefits in kind, which should be taxed. In some extreme cases, some think one is actually abusing company money when getting the miles for their own use, which may in the worst case even be considered illegal, but again, this is very country-specific.
In general, yes: you still earn miles for trips you fly regardless of who purchased the ticket. There are many frequent flyer programs around the world, each with fairly complex rules, so you'd have to check the rules of your specific program to know what caveats apply.
One thing that has changed a bit is that more airlines are selling their cheapest tickets in fare classes that don't earn you any frequent flyer miles (sometimes called "basic economy" in the US). These tickets generally come with other limitations (depends on the airline), like prohibiting changes, no advanced seat selection, or no carry-on baggage allowed. If a company is buying basic economy fares for job interview candidates, they're probably either incompetent or hate you, but you'd want to be aware of what fare applies to your ticket to know if you earn miles, and if so, how many.