The Mend were put together by Take That's former manager Nigel Martin-Smith. The music mogul is no longer in charge of the group, but still acts as their mentor.
A Digital Spy forum member complained: "Suppose it's just a coincidence they were put together by Take That's old manager.
"The show is disgusting and rigged."
The Mend features Kris Evans, Dean Kelly, Craig Worsley and Jay Kontzle. The band were sent through to Boot Camp after auditioning in Manchester at the weekend.
Describing themselves on Facebook, they said: "Together they are a Manchester based four-piece vocal group that produce, write, rap, sing, dance, you name it. They've been together for three years now, in and out the studio and rehearsing hard getting ready for 2011.
"The four together have created a fresh, urban soulful sound made up of all sorts of musical influences. They've worked alongside some incredible up and coming writers and producers."
An X Factor rep denied that Barlow's connections with Martin-Smith influenced the judges' decision on the group.
The X Factor auditions continue in Cardiff, London and Liverpool next month.
> Tulisa Contostavlos tips WAG for 'X Factor' final
> Louis Walsh in tears after 'X Factor' audition