If there are seven hundred thousand narrators whose life history has been recorded in the books of asma al-rajal through whom we have to glance the very word of Holy Prophet (May peace be upon him) than does this not mean that we are accepting, instead of these 12 persons (shi'ī imams) who are considered infalliable, whole seven hundred thousand persons as infalliale?
My answer to the above is: Not at all.
Please let me explain in a few bullet points:
1. Shia Muslims consider the 12 Imams to be infallible. They therefore do not find it necessary to rely only on the Ahadith that are reported from the Prophet (pbuh). This is why if you look at the Shia books of Hadith like al-Kafi, al-Tahzeeb, al-Istibsaar and Man La Yahzorahu al-Faqih you will find that the vast majority of the narrations end to one of the Shia Imams (usually the 5th and the 6th Imam). In fact you need to spend some time searching in the main Shia books of Hadith to find a Hadith that is narrated from the Prophet (pbuh). This obviously is because of the fact that Shia Muslims consider the Shia Imams to be infallible and the divine sources of religious guidance after the Prophet (pbuh). Obviously these narrations cannot be considered as Hujjah (indisputable reason and evidence) by non-Shia Muslims who do not hold the same belief.
2. Just as there are rijal (narrators) who have narrated Ahadith from the Prophet (pbuh), there are also rijal (narrators) who have narrated Ahadith from the Shia Imams. If you think accepting the narrations of rijal in non-Shia Hadith means believing that they are infallible, then you have to apply the same assumption to the rijal of Shia books (an assumption that is wrong, as explained in the next point).
3. Accepting a Hadith does not mean to believe its narrators are infallible. If you accept a news that some one gives you does that mean that you consider that person to be infallible? It actually only means that you have trusted that person for that news. Same applies to when people accept a Hadith. It simply means that they have trusted the narrators of that Hadith. There are many scholarly books that give us information about the life and degree of trustworthiness of these narrators (Shia or non-Shia) and there is a whole body of discipline that provides methods and ways to analyse whether a narrator or a hadith can be relied on.
4. The most important criteria for assessment of a Hadith is to compare it with the Qur'an and the Sunnah. Hadith on itself is not a primary source of understanding Islam. Only the Qur'an and the Sunnah are the primary sources of understanding the Qur'an.
Please do not hesitate to write to us if you like any clarification or if you have more questions about this subject.