The location had been Camp X-Ray - the high-security detention camp run by the US in Guantanamo Bay. Mr Ahmed, originally from Tipton in the West Midlands, was among several hundred foreign terror suspects held at the centre.
Mr Neely was one of his guards.
The scene of this current exchange of pleasantries couldn't be more different from where they last met - a television studio in London. Also here is Shafiq Rasul, a fellow ex-Guantanamo prisoner, without whose Facebook page the reunion would never have happened.
The journey of reconciliation began almost a year ago in Huntsville, Texas. Mr Neely, 29, had left the US military in 2005 to become a police officer and was still struggling to come to terms with his time as a guard at Guantanamo.
He felt anger at a number of incidents of abuse he says he witnessed, and guilt over one in particular.
Highly controversial since it opened in 2002, Guantanamo prison was set up by President George Bush in the aftermath of the 9/11 attacks to house suspected "terrorists". But it has been heavily divisive and President Barack Obama has said it has "damaged [America's] national security interests and become a tremendous recruiting tool for al Qaeda".
Mr Neely recalls only the good publicity in the US media.
"The news would always try to make Guantanamo into this great place," he says, "like 'they [prisoners] were treated so great'. No it wasn't. You know here I was basically just putting innocent people in cages."
The prisoners arriving on planes, in goggles and jump suits, from Afghanistan were termed by then US defence secretary Donald Rumsfeld as the "worst of the worst". But after getting to know some of the English-speaking detainees, Mr Neely started to have doubts all of them were fanatical terrorists.
He recalls how when he and Mr Ahmed chatted through the bars at Guantanamo, they had a surprising amount in common.
GUANTANAMO PRISON HISTORY
First inmates arrive at makeshift Camp X-Ray January 2002
Detainees refused rights of prisoners of war and right to a trial
Camp Delta, with more permanent facilities, opens April 2002
Some 700 prisoners eventually transferred to site
Many since been released or handed to national governments
By 2009, 215 men of various nationalities remain
President Obama concedes in 2009 his deadline for closing - January 2010 - will be missed
"It was no different from me sitting at the bar with a friend of mine talking about women or music," says Mr Neely. "He would say, 'you ever listen to Eminem or Dr Dre' and he threw off a little rap and it was just funny. I thought how could it be somebody is here who's doing the same stuff that I do when I'm back home."
Mr Neely was 22 when he worked at the camp and left after six months to serve in Iraq. But after quitting the military his doubts about Guantanamo began to crystallise. This led to a spontaneous decision last year to reach out to his former prisoners.
"I was pretty new to Facebook and decided to type in their names to see if their profiles popped up and I came across Shafiq's Facebook page. I decided to send him a little e-mail," says Mr Neely.
Released in 2004, after being held for two years, Mr Rasul and Mr Ahmed and another friend from Tipton had been captured in Afghanistan on suspicion of links to the Taliban. The three said they were beaten by US troops although this was disputed by the US government at the time.
After all that, the Facebook communique was a shock to Mr Rasul.
"At first I couldn't believe it. Getting a message from an ex-guard saying that what happened to us in Guantanamo was wrong was surprising more than anything."
To Mr Neely's astonishment he received a reply and the pair began an exchange of e-mails. It was at this point that the BBC asked if both sides would be prepared to meet in person.
Guantanamo: Jailer and jailed remember opening
Several months later the ex-inmates were sitting in the TV studio waiting to be reunited with their former jailer. But Mr Rasul was having doubts. He was feeling conflicted.
"There's a few people in my family who have said what do you want to meet someone like that for, the way he treated you, you stay away from him," says Mr Rasul. "They say because if it was me, I'd want to beat him up."
Mr Neely had also been feeling uneasy.
He arrived at Heathrow airport ashen-faced, pensive and reluctant to speak much before the meeting.
Mr Rasul and his normally gregarious friend were notably quiet as they sat in front of TV cameras waiting for Mr Neely to enter. No-one knew what to expect, and the atmosphere was tense.
After an initially awkward exchange about caps and jump suits, the conversation turns to the reason for the visit. Mr Neely says he'd thought about the moment a million times. He'd wanted to say how he'd felt complicit in their detention, and acknowledge the wrong they were subjected to.
But what were the pair doing in Afghanistan in 2001?
They explain that, being in their late teens and early twenties at the time, they had made a naive, spontaneous decision to travel for free with an aid convoy weeks before a friend's wedding, due to take place in Pakistan.
Mr Ahmed admits they had a secret agenda for entering Afghanistan, but it wasn't to join al-Qaeda.
"Aid work was like probably 5% of it. Our main reason was just to go and sightsee really and smoke some dope".
Does their former prison guard believe them? Yes, says Mr Neely, who says he thinks it was a case of "wrong place, wrong time".
Both sides are beginning to bond, yet towards the end, Mr Neely has a confession of his own. It threatens to destroy the mood of reconciliation.
He is deeply ashamed of an incident in which he "slammed" an elderly prisoner's head against the floor.
Mr Neely recalls that he thought he had been under attack because the man kept trying to rise to his feet. But weeks later he discovered the prisoner thought he was being placed on his knees to be executed and believed he was fighting for his life.
Mr Ahmed is speechless, then evidently conflicted as he wrestles in his mind with whether or not he can forgive. Eventually, he says he can.
But should Mr Neely be prosecuted for his actions? Mr Ahmed pauses again.
"He's realised what he did was wrong and he's living with it and suffering with it and as long as that he knows what he did was wrong. That's the main thing."
Afterwards, each say they had genuinely found some sort of closure from meeting. The sense of relief in all their faces speaks volumes, and they leave the meeting closer to one another.
Their story will be featured on BBC Two's Newsnight on Tuesday 12 January at 2230 GMT and in the documentary Guantanamo Reunited on BBC Radio 5 live on Thursday 14 January at 2200 BST.
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