Australian-born Dan, who qualifies for Scotland through his Ayrshire-born maternal grandfather, has struggled to win over the critics during his 14 caps under Williams and even came in for flak from the fans during the Scots' long-awaited victory over Italy a fortnight ago.
The clamour to bring back the Leeds Tykes player grows by the game but at a tense press conference in Stirling Williams insisted the debate between the two players was purely media invention.
He said: "I think this is simply a media story which is mounting pressure on Gordon and Dan and it's creating a problem which is simply not there.
"We're making a judgement based on what we're seeing in training and in international games which are different than at pro-team level. There are different demands and different pressures.
"There's not a lot between the two players. Gordon has played some for very good rugby for Leeds and when he gets his opportunity he has to take it.
"But obviously we are saying Dan has a wide enough all-round game to merit playing for Scotland.
"Dan made the only line break of the game against Italy. We moved 35 metres, got a penalty then kicked three points.
"But in international rugby, your number 10s don't make too many line breaks, maybe just one or two.
"I had a chat with Gordon and I felt sorry for him. I think we should just allow the young man to play and when his opportunity comes, allow him to take it."