I'm on Expedia and it does say that...however their policy seems to say that the airline could still charge a fee of their own in some cases.
They always say that, but it's not an issue. If they say free cancellation within 24 hours, that is what you get (usually until 11:59pm Pacific Time the next day IME. When you click on the itinerary after it is ticketed it should tell you how much longer you have to cancel for free).
Beware that if you try to cancel an itinerary BEFORE it is ticketed, you might not be able to do it online. I recently booked an itinerary that involved IB and BA on Expedia. A couple of hours later, I tried cancelling online, but was unable. I called to cancel and was on hold for a long time, and eventually needed to hang up due to Shabbos. I told agent that I am limited in time. I called back after Shabbos to cancel. At first I got some pushback with the agent saying it's past 24 hours (the official policy, though I had only booked on Friday morning, and this was the next day before 11:59pm). It took almost 40 minutes until they were able to cancel it. They said it was because PNR was locked by the airline, where it was sent for ticketing. They needed to get the airline to release the PNR back to them, and only then were they able to cancel.
The saga wasn't over yet. Two days later I see another charge on my CC instead of a credit. Another call to Expedia, asking for a supervisor, about 20 minutes on the phone, and credits were issued. All in all spent almost 2 hours on the phone to cancel and get refund.