The brahmana should give advice to the ministers or the legislators. They should be all qualified brahmanas, not paid man. Paid man has nothing to do... Even during the time of Maharaja Candragupta, emperor, he had a brahmana minister, prime minister, Canakya Pandita. He was not taking a single farthing as salary. When once explanation was called for from Canakya Pandita by Candragupta, immediately he resigned. "You cannot call any explanation. Then I resign." And he was living in a cottage, not that palatial building. He was living in a cottage. That was the system. Brahmana lived very humbly. He was not poor. Not that they are poor men.
(SB 1.7.34-35, Vrindavan, September 28 1976)

From the context it's clear that the explanation referred to why C.P. doesn't take anything from the king (who wanted to give him charity).

Before this story Prabhupad tell another story:

Not very long ago, say about two hundred or three hundred years ago, in Krishnanagara there was a big zamindar named Raja Krishnachandra. He went to a learned scholar, a brahmana pandita, who had voluntarily accepted poverty and asked him, “Panditji, can I help you in some way?”

The pandita replied, “I don’t require any help from you.”

“But I see that you are very poverty-stricken.”

“No, I am not poverty-stricken. My students get some rice for me, and my wife cooks it. I get some tamarind leaves. So it is very nice. I don’t require any help.”

The natural position of chanykya pandit is hard to fathom in our present ''polluted'' society.However in the past a brahamana of such incredible astute material and spiritual knowledge,was indeed a huge benediction upon a 'lower'' status king.He had such a profound influence on political and spiritual knowledge within indian culture that srila Prabhupada used to regularly quote his expert and revealing texts hundreds of years later.Still being relevant today provides us with a willing testimony of their authentic basis in spiritual and political sciences.

Without knowing all the details of the story, one thing that comes to my mind is that once the King had questioned Chanyaka's advices this could indicate that the King considered Chankya's advice to be tainted with some form of ambition or ulterior motive. This is not a good situation for Chanyaka because historically kings generally 'dispose' of ministers they suspect of ulterior motives.

From the Kings side, he should not consult a Minister who he doubts. There are many warnings in Artha-sastra and similar texts instructing kings to not keep any advisor close or take their advice if there is some suspicion as to their motive, and there are also several stories as to how a Minister has defeated a king by using the trust placed in him.

From Chanyaka's side, if there is suspicion or doubt on the part of the King, then the relationship of Minister and King cannot function properly as the King should intimately trust the Minister. If not, it is best a Minister leave such a situation. The detachment of Chanyaka is seen in that if he did have some ulterior motive, being the expert he was, he could have certainly provided the King with some satisifactory explaination as to why he gave a particular advice, but he did not. He walked away.

Since SP gives two slightly different versions, we'd have to see the actual details in C.P.'s biography or wherever this info is found.

The guy lived some 3000 years ago. Are you trying to read mind of someone who lived that long ago, he is a legend, while a real person and there is quite a range of views on him (obviously). Some say he was an atheist, some Vaisnavas claim him as a vaisnava. When Prabhupada was asked if he was a devotee, he said no.

The key answer is independence. Brahmana must be independent according to Srila Prabhupada, even never calling Canakya a Vaisnava would cite him a lot, and said that his 'name is still celebrated' even he was not a pure Vaisnava (my dear sri_govinda_das may have a vivid imagination on that, maybe read again your ref), but a great politician, very learned scholar, brahmana and great moralist. There must be brahmanas who are independent. Canakya Pandita, whose name is still, still celebrated, he was prime minister of Maharaja Candragupta, but he was not accepting a single paisa as salary. That was the, formerly, although there was monarchy, still there was a council of learned brahmanas and sages. They used to advise the king. The brahmanas did not take part in politics, but they gave advice, instruction to the kings, rajarsi. Imam rajarsayoh viduh. The rajarsi used to understand what is the values of life under the instruction of brahmanas, and they execute the order of the brahmanas. The people were happy. And because at the present moment such system is lost, people are confused and they are in frustration.

Just because Chanakyas (or Shankaracharyas worshipable deity) could be Vishnu, it does not make them Vaishnavas. There are different records of him in Jains (who claim him) and Vaidic records is brahmana, Jat or Ajivika (Ajivika adherents followed a strict regimen of asceticism, similar in many ways to practices undertaken by the Jains). While Chozhiars claim he was one of them. According to Jains Chandragupta gave up the throne and followed the Jain saint Bhadrabahu and died of starvation according to Jain tradition. But in any case there is no evidence of Prabhupada saying he was a devotee or a Vaishnava.