Nope. The pressure to DoJ for a SC can come from anywhere, and is effectively independent of the FBI.
In the Clinton investigation, the FBI as not conflicted. It could have and should have given the file to the DoJ. If not Lynch, then Lynch's deputy. It's up to Lynch (or her deputy) to decide if SC is warranted.
Comey usurped that. It's as if cop had investigated a murder but never informed the DA, because, in the cops opinion, no DA would press charges.
I've explained elsewhere, across a few threads, that I believe Mueller is a "Trump creation." Mueller (or somebody else) had to be SC in order to put Comey's witch hunt to bed, by somebody that the press could not spin into a Trump sycophant.
That's an unpopular view here, and I feel no need to repeat my justification over and over and over - meaning I have no interest in persuading people that I view as wring-headed, and I am grateful they feel no urge to persuade me.