This rumour has been circulating in the area for some time and I think that it's probably true. Knowing Haberdashers pretty well I'd be fairly certain that they wouldn't take the Beckham boys if they weren't academically able as regardless of money and fame if they couldn't keep up it would be very unfair to have them in a very academic school.
I'd say that Habs is an ideal choice for the boys. It's set way back from the road and there is no way of getting a glimpse of any of the pupils from the road. The school itself is set in the countryside so again, it is impossible to just wander in to the schoo and any unfamiliar faces would raise questions immediately. Whilst it's a private school it's not a public school so there are no aristocrats, just lots of hardworking parents from extremely diverse backgrounds so it's likely that the boys would be able to mix and blend in easily. It also has amazing sports facilities on site so there would be no need to leave the school at any time other than for matches.
It makes absolute sense that they brought the boys over from the US in January / February time as this was the entrance exam period and no doubt they were sitting just like all the other children vying for places.
Good luck to them.