McLaren is planning legal action against Red Bull for having, it believes, enticed Fallows to break a binding contract he had with the Woking-based outfit.
But amid high tensions over the matter at the Chinese Grand Prix, Red Bull team principal Christian Horner is adamant his squad did nothing wrong.
"The situation with Dan is very clear," said Horner. "Dan decided that he was going to leave Red Bull for reasons of his own.
"With the changes that have happened at McLaren [such as Martin Whitmarsh being moved aside], he decided that he didn't want to join.
"It was 100 per cent his decision to approach us and see if there was a situation still open.
"It was his choice and I think that getting lawyers involved, if that is the way that McLaren want to act, then that is what will have to be done."
Horner said he was unmoved by McLaren's threat of legal action, but he suggested that his rival would be better off focusing on making its car quicker rather than spending money on lawyers.
"It is very easy for McLaren to be drawing focus away from their bigger issues," he said.
"It is obvious why they are looking for aerodynamicists. I would have thought their focus should be a little bit closer to home."
And Horner also did not understand why Dennis suggested that the Fallows affair cast questions about Red Bull's honesty.
"I don't know how it can question the integrity of the team," he said. "It is the choice of the individual. Nobody can be forced to do a job.
"Slavery was abolished years ago and I don't think anybody can be forced to do a job against their will.
"Situations change - as Ron well knows. Probably more so than others, with the vast amount of experience that he has."
- Christian Horner
- Martin Whitmarsh