No.
What everyone is telling you should be read at face value because it's what we mean.
If you restore your phone via iTunes, iTunes will force your phone to update to iOS 7.1.2 which is the last version of iOS that the iPhone 4 is capable of running.
If you had an iPhone 4s you would be forced to iOS 8.3.
If Apple is not signing a version of iOS you cannot restore to that version. Apple stopped signing iOS 5.x years ago.
However, you have two things going for you depending on your circumstances.
First, iOS 7.1.2 is jailbreakable. So, if you restore and are updated to 7.1.2 you can still jailbreak.
Second, the iPhone 4 is the last modern iPhone than can actually downgrade. That is achievable through a bootroom exploit that was closed with the 4s. The kicker here though is that you will have needed to have saved your SHSH blobs for iOS 5.x in order to downgrade.
Now, the above is the general information I have on this. Someone else would have to walk you through it as I have zero experience in doing that.
I hope that answers your question.