Shia shaykh ar-Rawwad in his treatise “ar-Risala fi khabarul daif” (p42) quoted their master muhadith Abbas Qummi:
“and they don’t understand that IF chain (of report) is authentic that going to be a proof upon slaves, because report of truthful is a proof, and IF NOT AUTHENTIC, then IT IS NOT permitted to reject it due to possibility of coming from Ahlalbayt, and that would become a objection to them, as it comes in honourable report..”
Discussion:
1) Abbas Qummi apparently has no clue about terms of sound report in accordance to shiaizm. Or he used one from the “hundreds” available. Because if all reporters of hadith were thiqat (truthful) in accordance to shias is not enough for hadith to be sound (hujjah).
2) Here we have good example from known shia muhadith, that in reality THEY DON’T CARE about chain being sound or not, because even if it is not, they still shouldn’t reject it. It is good explanation of attitude which we can see from majority of modern shias. If hadith suits to their beliefs, they absolutely don’t care if chain of transmission is sound or not.
As a proof for our point of view, that shias has no right to reject any ahadeth, I’d like to cite a hadith from their book “Basair ad-Darajat”:
Translation:
from Abu Abdullah (alaihi salam): Don’t reject ahadeth which someone brought to you, because you don’t know, may be they are truth, (and by rejecting them) you would reject Allah beyond his Throne.
gift2shias.com 
1) What Sheikh Abbas Qummi (Aallaahu Maqaama) have stated regarding those Ahadeeth which are sound in terms of MATN (context) even if it is narrated through unauthentic Ithnaad, it shall not be rejected on ground of its being weak in ithnaad, if Matn is acceptable then there is no need to reject such traditions, like few Ahadeeth of Kitab Sulaym Bin Qays Al-Hilali (RA), in which all narrations have a common man in Ithnaad and that is Aban Ibn Abi Ayyash, who according to scholars of rijal was a Dha’if narrator, so anything narrated from him must be rejected, but few tradition in this book are acceptable because it doesn’t contradict authentic Taarikh after the death of Rasool Allah (saaw) written in both Shiah as well as Sunni Kutub. But few narrations in this book are absolutely unacceptable because of its contradictions with authentic Tareekh.
2) Majority of modern Shiah doesn’t accept a narration with weak chain, rather we just want those traditions which can neither contradict with Qur’an nor have an un-reliable source of narration. Few Shiah of Akhbari origin do accept traditions with weak chain of narrations, but even then they accept only those traditions which doesn’t contradict Qur’an or authentic Sunnah of Huzoor (saaw) and his pure Progeny (AS).
What about ignorant blind Sunni who believe everything written in Bukhari & Muslim, they can’t even hear a slight criticism against these books, if we Shiah criticize few narrations of these books, they eaither abuse us or threaten us. So modern Shiah are not like what you have stated, it is modern Sunni who acts like this.