While extant records do not indicate what gave offence, a reference in The Returne from Parnassus (II) suggests that Queen Elizabeth I herself was satirised.
The Isle of Dogs is a location in London on the opposite bank of the Thames to Greenwich, home of a royal palace, Placentia, where indeed the Privy Council met.
If I had thought the ship of fooles would have stayed to take in fresh water at the Ile of dogges I would have furnished it with a whole kennel of collections to the purpose."
The only party permanently hurt was the Swan's impresario Francis Langley, who alone among the play's producers was not able to obtain relicensing.
The 28 July order does not mention the play; it was written in response to one of the city authorities' periodic pleas for an end to the theatres.
In this light, Pembroke's men may have made their offence worse by performing the play (wittingly or not) after the date of prohibition.
Andrew Gurr adds to this picture by noting the tendency of the Court to license two chief companies throughout the later Elizabethan and early Stuart periods.