No, you don't need to trust anyone. You can verify how the accumulator works before compiling your code if you like. (ignore back on.)
We will be able to verify how the accumulators works with the opensource code but the problem is no that.
The problem is that Gnosis will generate the keys (RSA) of these accumulators.There is nothing trustless. You need to trust that Gnosis is honest and will not keep the factors to forge zerocoin proofs and then infinite ANC.
Source:
https://wiki.anoncoin.net/Zerocoin#Zerocoin_in_practice (Section: Criticisms, fourth paragraph)
If gnosis has his own rsa ufos - with factors - then he had 8 core years squirrelled away in his basement ? get real !!! You cannot fake the numbers nor the work needed to work them out.