Dublin chairman Andy Kettle has responded by saying they will "bend over backwards" to facilitate county players with the talent and desire to play both codes - but he reckons that to do so at senior level has become a virtual impossibility.
O'Grady's appeal was obviously prompted by the news that Ciarán Kilkenny - having returned from his shortlived Aussie Rules career - has committed to the Dublin senior footballers, but not the hurlers, for the coming season.
The Castleknock prodigy has, however, indicated his availability to the Sky Blue U21 hurlers for their summer campaign.
"It is great to have Ciarán Kilkenny back again and I think it is critical that he is facilitated to play at least U21 championship this year. The same applies to Cormac Costello," O'Grady told the Evening Herald.
"I believe that it is the responsibility of the county board to ensure that dual players are given the chance to play both games. A lot of money has been invested in these players over the years.
"And it is certainly not good business if they are not given the opportunity to play hurling as well as football."
Contacted for a county board response, Kettle declared: "The most important people in this whole debate are the players themselves.
"The county board will facilitate, in any way possible, any dual player who expresses a desire to play both codes - as we do up to minor level.
"History has shown, in the last few years, that when players come out of minor level they tend to concentrate on one code or the other.
"There have been a few exceptions - Rory O'Carroll played U21 hurling versus Kilkenny in a Leinster semi-final, (2010) but did not play any further part in the campaign.
"The county board will bend over backwards to facilitate, and all county managers tend to do so too," Kettle maintained.
"The people who finally make the decision are the players themselves. To quote somebody, it's better to be a willing horse than an unwilling horse. A willing horse will go the distance for you. To try and force someone to do something is counter-productive."
However, the modern reality is that senior dual stars (a la Teddy McCarthy, Seán óg ó hAilpín during his younger days, or Conal Keaney for one season for the Dubs in 2004) are an endangered species bordering on the extinct. Eoin Cadogan has been a rare beacon, but even he has decided this season to focus solely on the Cork footballers.
It's equally apparent, whatever is said in public, that county managers far prefer having exclusive access to such players.
Kettle contended: "Personally, I accept it is virtually impossible to do both codes (at senior level) because the skill level in both games at the moment demands 100 per cent commitment to either code.
"If someone is trying to divide their time, it's possible they will fall between two stools."
As for Kilkenny's commitment to the Dublin U21 hurlers, the chairman added: "I personally heard Jim Gavin say he didn't see any problem with that.
"Again, at this stage, let's not jump fences. Jim Gavin hasn't finalised his panel. It was always his stated intention to have a panel of 30 players. Depending on whether a player is in or out, that could influence a decision to play either code."
And while Cormac Costello has yet to publicly indicate his intentions regarding the U21 hurlers, Kettle concluded: "I'm sure (U21 manager) Shay Boland will be talking to him."