As seen in this section of Adi Parva , Drupada's words when Drona came to him were
Then the son of Bharadwaja, endued with great prowess went to king Drupada, and approaching that monarch, that tiger among men, said, 'Know me for thy friend.'
Hearing this Drupada said, 'One of low birth can never be the friend of one whose lineage is pure, nor can one who is not a car-warrior have a car-warrior for his friend. So also one who is not a king cannot have a king as his friend. Why dost thou, therefore, desire (to revive our) former friendship?'
The same section mentions there is friendship between their fathers. Moreover Drona found merit in Drupada's words, and therefore after winning over the kingdom with the help of Pandavas he too reiterates the same when returning half the kingdom back to Drupada.
If what they say is true, then does it mean that their fathers had it wrong ?
Related question: The popular story goes that Drona approached Drupad because his family was in dire straits. Is there reference to it in any other part of KMG Mahabharat or is it just another creative interpolations of our times?
EDIT Previously the question was asking for the basis of saying low-birth and pure lineage matters when it comes to friendship. Understood that is not the case