Internacionale and Au Naturale founder Ken Cairnduff, a member of the pro-independence campaign group Business for Scotland, was interviewed on BBC Radio Scotland's Good Morning Scotland show on Thursday.
He and another guest were introduced as referendum voters "who have yet to make up their minds".
They were questioned on what might sway their view in favour of a Yes or No vote.
The entrepreneur - who is described as a "passionate" independence supporter on the campaign group's website - called for a live TV debate between Alex Salmond and David Cameron, a key SNP and Yes Scotland demand.
He was asked by presenter Gary Robertson if he was "genuinely undecided" but ducked the question and failed to declare his membership of Business for Scotland.
Scottish Labour has complained about the broadcast.
A party spokesman said: "We have long worried about BBC Scotland's coverage and have made a series of observations and complaints, which have been ignored."
Asked about his appearance on Good Morning Scotland, Mr Cairnduff said: "This is all a fuss about nothing."
A BBC Scotland spokesman said: "We have been made aware of this claim and we are looking into it."