Owners didn't overrule Rodgers. If anything Rodgers overruled them!!! I jest 
It was joint decision between the board and Rodgers. If Rodgers really and truly wanted Remy THAT much he'd have took the risk. But he didn't.
I don't know what the risk would have been so don't to ask me!
FSG have history or renegotiating a contract when medical issues arise. Obviously Rodgers knew of Remy's heart condition, Ayre, I wouldn't put money on it and I somehow doubt the owners would initially.
It wouldn't surprise me if they tried, or wanted to at least, renegotiate the contract offer in some way - shorten it, offer a lower basic and load it up with bigger appearance bonuses etc.
There has to be a big difference between Remy's heart at 24 and at 32/33, or the effects it could have.
Either that or there's a nagging concern over his overall fitness or ability to avoid minor niggles becoming more serious. He missed 17 games last season for Newcastle, including the last one of the season against us, and he seems to pick up calf and ankle problems. He was out for the start of last season with Newcastle, all of August, then again March to April, allegedly with either a recurrence or re-injury of the August one and then the last game of the season.
My money would be on the owners' unease over his heart as Rodgers seemed to choose his words very carefully, but quite specifically as well:
"We have made a decision, as a club, not to go ahead with the deal". The club have made no 'official' mention of failed medicals, but neither have they done anything to deny what's been reported. It's as though the media have given them a convenient reason to shelter behind.
The original reason for the delay was a hold up with paperwork, indeed, the owners had yet to sign off on the deal once his heart condition became known to them.
All the reports had him passing a medical, for example:
http://www.mirror.co.uk/sport/football/transfer-news/loic-remys-protracted-liverpool-transfer-3916218#.U-VQI6NCx74"
Remy passed a medical in Boston on Wednesday and has agreed a four-year deal worth around £80,000-per-week.http://talksport.com/football/remy-update-qpr-strikers-move-liverpool-delayed-claims-pearce-140724103531Interview with Echo's James Pearce who was out in America with the team. Interestingly, it's quite guarded, almost skips the subject.
It's just a real shame it didn't happen, for
whatever reason, at least from a footballing perspective.