He was an oddity to his new team-mates then: unmistakeably British, tea-drinking, highly-educated and with a line in sarcasm which went over the heads of most Americans.
With eyebrows raised already, to reveal one further trait might have seemed trivial. To declare to the room that he was homosexual would not have been a big deal, right? "That would have been inconceivable," says the former basketballer, shaking his head. "It was 1995. The laws criminalising gay people were multiplied by 10. I would have lost my job instantly."
Jason Collins, who ended the current NBA season with the Washington Wizards, came out as gay two days ago to huge fanfare and a wave of support – from the league, from colleagues past and present, and from Amaechi, with whom he has sought regular counsel since deciding to be open about his sexual orientation. It is a positive sign of change. But while Amaechi attests the UK society has a broader liberal streak than that in the United States, British football has not yet met its torchbearer.
The tragedy of one-time Airdrieonians striker Justin Fashanu reflected a less tolerant age. The frightful abuse which pushed him to suicide came to mind with the news that USA winger Robbie Rogers felt obliged to retire after coming out two months ago, rather than go back on to the field. Soccer, in both Scotland and England, has worked to cure many of its ills. But in the eyes of Amaechi, there is still too much cheap talk and not enough action.
"In football, they're in cloud cuckoo land," he says scathingly. "They think that a marketing campaign is the same as a change campaign. As a psychologist, I can tell you that's not true."
Charters are not in short supply from the myriad bodies with influence; the Scottish Football Association has its Equity Policy, while its English counterpart has a more targeted campaign known as 'Opening Doors and Joining In'. "B*******," says Amaechi. "Football is the bloody Saatchi and Saatchi of sport right now. They do posters and flowery rhetoric better than anyone else. And they do change worse than all of them."
The former England player, who currently spends most of his time on management consultancy and political advocacy on both sides of the Atlantic, states firmly that progress must come from within. "I wonder when supporters are going to start getting p***** off," he adds. "Because, essentially, football powers will be making out that the problem with homophobia in football is actually those working-class – read 'stupid' – fans."
Supporters are not blameless, of course. Brighton and Hove Albion's fans frequently complain of homophobic abuse, Tottenham Hotspur's followers of anti-Semitic chanting and then, of course, there is the lingering sectarianism that coats the Old Firm in Scotland.
"Do we need to get rid of some of the fans? Sure," says Amaechi. "But those fans are led by the nudge-nudge-wink-wink approach that some of the officials take, where you can hire the comedian like they did at the PFA [Awards, when Reginald D Hunter was criticised for using racial humour]. I remember going to their awards a few years ago and walking into the room and thinking: 'the only [other] black people, outside of the players, are a knight in Sir Trevor Phillips and a peer in Lord Ousley. And the only women were on the arms of the players.
"I listened to the comedian they hired that year who thought it was acceptable to talk about 'poofs and faggots'. That's who these people are. Until fans and the media start holding them accountable, they will keep putting out more posters, which is cheaper and easier than changing personnel."
Collins, a fine man and a respectable player, will now be the best judge of whether the NBA can stay ahead of the game and if, for all the soothing reassurance he has received, there remains a less-accepting core of players who will choose to exclude him.
It should be noted, he is currently without a team. At the age of 34, and with his best years behind him, his sexual orientation might not be the only barrier to surmount if he is to become the first openly gay player in a major American league.
There is evidence that the locker room can be a tolerant environment, though, with Amaechi finding that his team-mates would often codify their acceptance. "On one long trip, Monty Williams [then his team-mate at Orlando Magic] says: 'Meech, you don't talk about women a lot.' And I said: 'Indeed.' He put his hand on my shoulder, went: 'Cool' and then walked off. And that was it."
In football dressing rooms, there will doubtless have been similar confidences shared. More difficult, conversations may yet be required for sport to remove the closet door, though.