Didn't he successfully sue The Sport newspaper for these very same allegations?
Yes he did.
He received £40,000 damages and £60,000 legal costs.
In 1991 £40,000 could have bought you a house in many parts of the UK.
What the Sport alleged was that his gun was at the property on the night of the murders and that it might have actually been used in the murders.
The matter was not tested in Court - the Sport took the commercial decision not to contest it.
The choice they faced was to pay the £100,000 to end the matter or pay £500,000 in costs to contest it.
If they won Anthony would not have had the £500,000 to pay them.
They obviously believed what they printed - they had informed the public of this real possibility - but they decided not to waste £500,000 with the lawyers.