I'm sure that's the reason.
So why would you want that institution to perform your burial service?
And I would point out that once the church made it's position clear and revoked it's offer, Mr. Sinclair's family didn't ask for anything from the church nor did they accept anything from the church. So your question is moot. They didn't want that institution to perform the burial or have anything to do with it.
But the question still remains why the church extended the invitation in the first place? They knew who he was. Did they expect the family to deny it as the price for allowing the service there?