"Please note: Dual or concurrent training courses and testing are not accepted by the authority. All training must be undertaken specifically for an EU Part-FCL license, as stipulated in FCL.005 and its associated AMCs and GMs. While an EU Part-FCL course may be recognised by third-country authorities, the IAA only accepts courses conducted in full compliance with and intended for EU Part-FCL licenses, ratings, approvals, or certificates."
Whoever wrote this nonsense should go back to drama school. The IAA has no legal authority to curtail the recognition of training and testing by other sovereign authorities outside of the EASA system. Refusal to grant a licence/rating/certificate based on what another authority accepts would itself constitute a breach of EU law. There's no enabling provision for this in the Aircrew Regulation.
The rest of the IAA's email is unhelpful. Competent authorities have the power under art 3(b) of Regulation 2020/723 to credit third-country night rating holders, whose prior experience and knowledge is at least equivalent to that required for the Part-FCL NR, subject to a recommendation by an EASA ATO/DTO.