John Smedley's twitter account has a bunch of posts about the launch of H1Z1 in early access (thanks IncGamers). A tweet replying to a complaint about "the airdrop P2W issue" offers a refund, and this is followed by word they are offering "no questions asked" refunds through Monday. His most recent tweet on the topic says they have asked Valve to honor refund requests this weekend, which follows this tweet pointing to a reddit post with more on their policy:

Hi folks,

If you feel like the airdrops are an issue for you, you may immediately request a refund to bwilcox@soe.sony.com - this offer applies till Monday and it applies only to people that have purchased the game as of 10:30am Pacific today 1/16/2015 -

Please note that this is going through us, not Steam. Which means it's a little more work so please be patient with the actual refund (it may take a day or two).
Smed