"What has happened ... has happened by accident. We met, negotiated and found some common ground," Cheika said.
"We didn't target him."
While the dithering NRL was unwilling to budge on a salary-cap showdown with the Eels, the Australian Rugby Union was happy to support the Waratahs' desire to sign Folau.
The scenario suggested money was the major motivation for Folau, a charge sternly rejected by the 23-year-old.
"I walked away from the AFL deal which was massive," said Folau, who declared he made no promises with Eels' coach Ricky Stuart.
"I spoke to Ricky about the possibility of coming back to play rugby league.
"Some contract things didn't work out ... and I couldn't wait any longer, sitting around.
"He (Cheika) really got me going and got me interested."
Folau's former boss was scratching his head at how Parramatta failed to come to terms.
"I think most people are very, very surprised that the NRL and Parramatta didn't do a deal," GWS chief executive Dave Matthews told the AFL website.
"I think they trumpeted his return, based on the confidence they'd shown. They have missed out because he's an outstanding athlete and tremendous role model.
"You won't find anyone at the Giants or anyone in the AFL questioning his integrity."
Stuart led a chorus of criticism of Folau, who said he was shocked to be tagged as a mercenary by some pundits.
Cheika, who spoke glowingly of Folau's values as much as he did his aerial leap, said the code-hopper's character should not be called into question.
"They really wanted him to play. It's unfortunate for them it didn't happen," Cheika said.
"Obviously there were limits on what they can do and the timeframe they could do it in."
Folau was relaxed and confident about his second code shift, declaring long-term goals and saying there would be no reason for him to leave the 'Tahs if he enjoys next season.
"Obviously it'd be great to represent your country and to play against the likes of the All Blacks is something that's appealing," he said.
But the former rugby league Test and State of Origin centre recognised the work required, as did Cheika.
"He'll just have to catch up. The other blokes are running pretty hard," Cheika said of the seven weeks of pre-season training Folau has missed.
Folau will train with the franchise for the first time on Thursday.
- AAP