In my experience, many diagnostic and S.M.A.R.T. utilities have a lot of false negatives.
While it is definitely not fool proof, I think that if you have the symptoms of a HDD failure, it is most likely a HDD failure. Of course, it could be something else....
I purchased a BTO Late 2012 27" iMac at its launch, and maxed out most of the options that I couldn't (easily) upgrade myself later. I decided to get the 1TB Fusion, as it was a good balance of storage and speed for me.
A little more than a year in, I started having what appeared to be subtle HDD related issues. Usually a restart would fix he issues, and they were very infrequent that I wasn't really concerned. As time went on, the symptoms started happening more frequently, and restarts would hang, and then sometimes it would take multiple restarts to get things back up and running.
All the utilities I tried, and Apple's HW Diagnostic test showed everything was good. A reinstall of the OS seem to fix everything, but that only lasted a few months, so about 1.5-2 years in, I contacted Apple Support, told them the symptoms, which they agreed that it was most likely a failed HDD.
I was set up with what end up being the first of many Apple Store visits, which they used a few diagnostic tools and said that it was SW related, as their tests showed the HW as being fine. I didn't agree, but not much I could do. They wiped the Fusion Drive, and I drove the hour trip home with my freshly wiped iMac.
The symptoms and boot hangs came back in about a month, which I started the process over again with the Apple Store. Same thing happened as last time, and again, I went home with a wiped drive.
This happened a few more time, but less time in between each time. It got to the point that the drive wouldn't boot after a day of being wiped.
Talking to Apple support on the phone, and talking to the Apple Store people was like two separate conversations. The Apple Support phone calls seem to agree with me that the HDD was the problem, but the Apple Store refused to replace the drive stating that their HW test showed the HDD as passing.
They offered to do an extended test, which would last 5 days and I could pick up my iMac a week later. Of course, it passed their extended test, and I went home with a wiped drive.
I was getting increasingly frustrated, especially as my AC warranty was ending soon, but luckily the drive fully failed to the point that it wouldn't boot into anything, including internet recovery nor the Apple Store's diagnostic tools.
They finally agreed to replace the drive, and I had 12 days left of my warranty. No problems since.
The point is, I tried many different tools, and the Apple Store also used their diagnostic tools, and the clearly failing drive passed every test.
I have seen diagnostic tools give false positives on other Macs too.