Retirement tax questions

The 1099-R you got from Fidelity was correct.  Distribution Code G would only apply if this were a direct rollover - Fidelity moved the funds from a one retirement account registered to you directly to another retirement account registered to you (at Fidelity or another IRA fiduciary like Vanguard).

Since Fidelity distributed the funds directly to you and you moved them into another IRA account (even if held  by Fidelity) then Distribution Code 7 was correct. 

That could not have been the case since they withheld taxes from the distribution they made to you.

The 1099-R interview for the 1099-R, asks "What did you do with these funds?" If you answer that "you moved the funds to another retirement account", you won't be taxed on the rollover.

See the following screenshot: