Ahlul Khibra are the experienced scholars in the Hawza who have the full ability to evaluate the standard of knowledge of highest scholars and give scientific opinion about who is the most knowledgeable among all the scholars. They do not need to be Maraaji' themselves. They are not any normal scholar or intermediate students at Hawza.
There are many Sunni scholars by this name. Ibn Al-Arabi Al-Maaliki (Abu Bakr) ( Died 543 Hijri) is a Sunni Shaikh who wrote Al-Awaasim Minal Qawassim العواصم من لقواصم. He was the person who claimed that Imam Husain (AS) by fighting against Yazeed, went against the teachings of his grandfather the Prophet (SAWA). He was clearly away from Ahlul Bayt (AS) and follower of Bani Umayyah who were ruling Andalusia where he was living.
Ibn Arabi (Mohyiddin) (Died 638 Hjri) , the Sufi Sunni scholar, is a different person who wrote Al Fotoohaat Al-Makkiyyah الفتوحات المكية . His books contain right and wrong things as he was not strictly following Ahlul Bayt (AS). He wrote some statements praising Ahlul Bayt (AS) but also wrote praising some enemies of Ahlul Bayt.
We have to be very careful when we read for such persons.
Which claim is to be countered?
Please write it clearly.