The newspaper denies the allegations.
However, given that a central issue is whether the Daily Star can tell fact from fiction, I was rather amused to see this firm denial included in its response to what they clearly see as the rather shocking and offensive idea that the national title would be negative to Muslims or endorse the EDL.
For the record, the Daily Star editorial policy does not hold any negativity towards Islam and the paper has never, and does not endorse, the EDL.
Up to a point, Lord Copper.
To proudly declare that the Star "has never" endorsed the EDL is to stretch sophistry to the limits.
If the Daily Star wasn't endorsing the EDL in its extremely positive news and editorial coverage, what we can say with confidence that any party would be praying for more "non-endorsements" where those came from, as shown by the delight and pride of EDL supporters in response to the paper's coverage.
The EDL was treated to that rarest of things - a Daily Star front-page politics splash heralding the (apparently unfounded) claim that the EDL was planning to put up candidates. This news report included the claim that 98% of Star readers backed the party in a (totally unscientific, of course) phone-in "poll".
The non-endorsement continued with a very positive "Don't ignore the EDL" editorial to boot too, which was reproduced on the Guardian website.
"Critics say the English Defence League is a racist, extremist organisation that's filled with hate. The group's leader Tommy Robinson strongly denies this. He says members have no problems with race.
But he admits he is against 'barbaric' Islam and the way it affects Britain. Whatever side of the fence you fall, one thing's for sure.
There is a visibly growing support for the EDL. It is attracting people across Britain to its ranks who feel the same way.
Full text of editorial
To be fair, the EDL-encouraging editorial was somewhat more measured and couched in less celebratory tone than, say, the Daily Mail's infamous 'Hurrah for the Blackshirts" editorial back in 1934.
But the central motivation - to challenge claims of extremism as politically motivated, so as to legitimise the far right group as decent common sense patriots - is similar. The Mail then was explicitly in favour of Mosley's fascist party taking the reins of government. The Star's non-endorsement simply wanted to endorse the EDL's concerns at this stage, celebrate their growing support, and to warn of dire consequences should this be ignored by the major parties.
Somehow, all of this positive coverage seems to have given rise to a perception that The Star was championing the EDL. The Jewish Chronicle in its article Star no longer shines on the EDL certainly seemed to have got that idea, reporting that propreitor Richard Desmond had not had any prior knowledge of the editorial decision to cover the EDL so positively in the paper's news and editorial coverage.
The paper then appeared to shift to a more critical tone after its news and editorial promotion of the EDL drew attention.
So the Star statement suggests that it won't be championing the EDL again.
Because - remember - it never has.
The question of "negativity towards Islam" (it is negativity towards Muslims which people worry about) is perhaps rather subjective.
As these front-pages from the Star and Express may suggest, you shall have to make your own minds up.
Since the Daily Fatwa spoof was pulled at proof stage from the paper after a staff revolt argued it was "deliberately offensive" to Muslims, should not the paper's management claim credit for its sensitivity on the issue. (I did wonder whether splashes like "BBC puts Muslims before YOU!" might, inadvertently, imply a mindset that you couldn't be a Star reader and a Muslim, which seems odd, given the absence of negativity towards Muslims in the newspaper).
And mistakes do happen in a fast-moving news environment, as a PCC judgement against a Star front-page article shows.
The front-page article reported that a Rochdale shopping centre had installed "Muslim-only squat-hole loos", and that the local council had wasted "YOUR money" on them ...
In this prominent story, there were two clear errors of fact which, in the circumstances, would have misled readers in a significant manner: the toilets could not be described as "Muslim only"; and were not paid for by the local council. While the newspaper had accepted that the article was wrong - and offered to correct the item - the Commission was particularly concerned at the lack of care the newspaper had taken in its presentation of the story.
The Star ran this correction to retract the waste of public money on Muslim-only loos story:
Our 15 July article said that squat style loos at Rochdale Exchange Centre were for Muslims only and were a waste of the council's money. We are pleased to make clear that the loos may be used by non-Muslims and that they were paid for by the developer.
The Star recently withdrew from press self-regulation through the Press Complaints Commission, along with the Express titles.
The jury is out on whether - without external regulation even from within the media club - the newspaper has identified some more robust ways to ensure its reporting is more accurate than on that occasion.
Perhaps it would move just as quickly to correct any future omissions should mistakes of this kind where completely made-up nonsense is used to stir up grievances somehow again creep into the newspaper in future. But perhaps they wouldn't.
Let's just say that the Star's rebuttal statement does not entirely secure confidence that telling fact and fiction is yet an in-house speciality at the Daily Star.