I’m highly skeptical of this claim since there’s a cost to running any system. It seems more likely that they just made fees implicit rather than explicit (as in Bitcoin) but, regardless, someone needs to be paid to keep servers running.
Then there is a price; it's just measured in watt-hours of energy spent instead of denominated in cryptocurrency.
Unless the cost of verifying transactions is zero, this just means that the cost is now measured in CPU cycles at the client. In the end, this may be higher than whatever you pay with Bitcoin, depending on how much work you need to do. This is what I mean by "making fees implicit" - there's still work to be done, but not putting a price on this work doesn't mean it's free.