Without going to fallible and biased human explanation , if we restrict ourselves only inside the Quran a pure guidance for getting the right explanation , we will come up with the right meaning of Ahle-Dhikr .
Read the first verse adjacent to its sister verse :
[016:043] And We sent not (as Our messengers) before thee other than men whom We inspired - Ask the ‘Ahle-Dhikr’ if ye know not! -
[016:044] With clear proofs and writings; and We have revealed unto thee the ‘Dhikr’ that thou mayst explain to mankind that which hath been revealed for them, and that haply they may reflect.
Two points to mention here :
01- The second verse [16:44] automatically detects the word ‘Dhikr’ as the Quran since it was revealed to the Porphet Muhammad (p) . Hence ‘Ahle-Dhikr- actually refers to ‘Ahle-Quran’ who 100% restrict their selves inside the Quran for any issue to work out .
02- Second verse also tells us that the duty of the Prophet and also the duty of ‘Ahle - Dhikr’ to explain from the Quran only on any issue they are asked . Hence . They have no option to answer the questions they are asked from any other source than the revelation of Allah , the Almighty .
Now let us see the second verse :
[021:007] And WE sent none as Messengers before thee but men to whom WE sent revelations. So ask the ‘Ahle-Dhikr’, if you know not;
[021:008] Nor did We give them bodies that ate no food, nor were they exempt from death.
[021:009] In the end We fulfilled to them Our Promise, and We saved them and those whom We pleased, but We destroyed those who transgressed beyond bounds.
[021:010] We have revealed for you (O men!) a book in which ‘Dhikr’ for you: will ye not then understand?
Again verse 10 refers the word ‘Dhikr’ as used in ‘Ahle-Dhikr ’ . Almost like the previous sets of verses , i.e., 16:43-44 , the word ‘Dhikr’ here detects the messages of the Quran .
Therfore , from those two verses which refers to ask ‘Ahle-Dhikr’ are actually addressing t to the ‘Ahle-Quran’ who will answer any interrogations from the Quran only and will not use any other external source than the Quran .
Some other verses can be added in this discussion to do a ‘double-proof’ the view I described above :
01. ‘Dhikr’ is one of the many noble titles used by Allah , the Most Exalted to refer His book Quran . Here are the list of some verse where you can find this title ‘Dhikr’ referring to the Quran : 21:50,39:69,41:41-42,3:58,12:104,15:6-9,43:43-44 etc. Therefore to call ‘Ahle-Dhikr’ as ‘Ahle-Quran’ or ‘the follower of Quran’ is quite justified and appropriate .
02. Allah , the Almighty clearly instructs us to answer on any question regarding Islam by using His revelation , the Quran only . Double check the verse on this facts :
[005:101] O ye who believe! Ask not questions about things which, if made plain to you, may cause you trouble. But if ye ask about things when the Quran is being revealed, they will be made plain to you, God will forgive those: for God is Oft-Forgiving, Most Forbearing.
Therefore 'Ahle-Dhikr' are in fact 'Ahle-Quran' who answer any inquisitions from the Quran only .
03 . Read the following verses carefully :
[005:048] To thee We sent the Scripture in truth, confirming the scripture that came before it, and guarding it in safety: so judge between them by what God hath revealed, and follow not their vain desires, diverging from the Truth that hath come to thee….
[005:049] So judge between them by that which Allah hath revealed, and follow not their desires, but beware of them lest they seduce thee from some part of that which Allah hath revealed unto thee. And if they turn away, then know that Allah's Will is to smite them for some sin of theirs. Lo! many of mankind are evil-livers.
In the above mentioned verses, with a grave tone and massive importance Allah , the Most Majestic ordered Prophet Muhammad and his followers to implement any rule or laws just according the Quran . In those verses Allah , the Most High forbids not to follow any other laws or creeds made of any other human . Also it is said ‘but beware of them lest they seduce thee from some part of that which Allah hath revealed unto thee’ which means that even for a tiny issue we must reject any human-made law and turn back for the same to Allah’s revealed word .
Therefore If Ahle-Dhikr needs to reconcile any issue between two disputed parties they must turn their attention to the Book of Allah to solve it . They have no choice to use external elements to have the reconciliation.