‘Receive us’: really the term means, be open hearted to us, make room for us. It does not mention the heart, but that is what is implied.
We were reading not so long ago of a certain so-called minister in the USA who has created a mega church, in which he abused people with his rough talk and his bullying. That could not be said of the apostle. ‘We have wronged no man.’ That so called minister corrupted people, but Paul could say, ‘We have corrupted no man, we have defrauded no man.’ The false teachers on the other hand had done all those things.