Giving you a private key is better in theory, but it also carries another risk, because you have to trust the service to not use it asap after they give it to you.
It is no more risky than any other method. You still have to trust the mixer with your coins, and a mixer can just as easily claim that you sent coins to a phishing address as they can claim you already claimed the private key.
If the Mixer has little BTC or is new they might not have funds on another chain to send to you and then they just forward your BTC back to you which has the same trail.
This is a genuine concern, and even with a lot of intermediate transactions bitcoin can still be traced through a mixer. There was a great post a few years ago here -
Breaking Mixing Services - which demonstrates exactly that.
It's worth noting that ChipMixer behaves differently to all other mixers and so is more secure in this regard. When you send coins to ChipMixer, you are given back chips which can be redeemed for bitcoin outputs which are already funded. So if I sent 0.1 BTC to ChipMixer right now, the funds they give me in return are from address which were funded in the past. There is no possible way they can return the same coins back to me.