Essentially, the answer is YES. PCI DSS certification of a merchant is not related to its acquirer. However, in many cases, if you want to become a payment gateway, payment service provider, or a payment facilitator, and partner with an acquiring bank, this bank may require you to have an AOC (attestation of compliance) cetificate, that is itself a result of PCI DSS certification. You get this certificate through third-party PCI assessors, such as SecurityMetrics, Coalfire, Trustwave etc.
If you are dealing with an acquirer and it is constantly asking for PCI DSS compliance, it means that it just needs you to have an AOC in order to start technical integrations. However, it’s not the acquirer you need to address, to get this AOC.