When GrandCom entered the BPO market as a technical outsourced provider, with a workforce spread over the US and South Africa, we too were hesitant as the failed attempt of using outsourced offshore services was experienced by us as well.
We were hesitant at first in offering outbound solutions for this reason. What we discovered though, was that an accent was not the problem but the comprehension and lack of a westernized mindset caused a disconnect when offering solutions to westernized clients.
We used South African staff to cover the shifts that were not ideal for US staff and were happy to find that the accent was never an issue.
For this reason, the first step in choosing a provider is choosing a partner that offers staffing that has comprehension of the language to the same level as the people they will service.
The majority of South Africans have English as a first language and the majority of entertainment is sourced from the US. Meaning, shared cultural understanding and values.
Making use of South African staff for instance, to service the Latin American community, would not make sense. But making use of staff from English-speaking countries (such as the US, UK, Canada, South Africa, New Zealand, and Australia) works when servicing other English-speaking countries. This is one of the reasons we strictly take on new clients that we are comfortable we will be adding value to and the provider you choose needs to have this mindset.
A big warning sign would be any sign you have during the initial stages of choosing a provider, that cultural nuisances are not picked up on as well as any comprehension issues, whether large or small exist when the provider repeats back what they see your requirements are. If you pick it up, your clients will as well.