South Africans reacted with anger when the news broke on Monday but Safa spokesperson Dominic Chimhavi said they could not impose a technical team appointment on Baxter.
“We don’t interfere with the technical team because the head coach has a right to chose whoever he wants to work with‚" Chimhavi said.
"The only thing that we were concerned about was if Chiefs‚ given their situation [with goalkeeping injuries‚ and struggling in form] would release him.
"They've been good enough to do that‚" he said on Monday after his decision.
"So if anybody sees it as anything else than the best and most viable decision that we could make‚ I'd be massively surprised.
"It's not as if I've run out and roped my son in the second he's landed in this country. He's been working with Chiefs and with SuperSport.
"And people maybe always will have opinions. And they don't always have to be well-founded. Never let the truth get in the way of a good moan.
"I don't expect it to be a decision that is attacked by the people who understand football.
"But does that mean it won't be attacked by certain people - well‚ it may do.
"But I'll be massively disappointed and surprised if people don't see it for what it actually is. It's the best decision in a very difficult situation."
Arendse‚ Bafana's goalkeeper coach‚ pulled out of the camp a few days ago due to family commitments.