It is a possibility. The fault shown in that bulletin; P132600 (connecting rod knock) will illuminate the check engine light and cause reduced power mode, however it does not explain the vibration you felt.
P132600 and misfire faults must occur during two consecutive trips to be recorded as a confirmed fault. The first occurrence is considered a pending fault. Pending faults are not saved in the computer memory for long, this is why your mechanics do not see any stored malfunction data.
There’s absolutely no good reason why a shop should do that, imo
All it will do is make a customer who isn’t familiar with the tool even more confused
I don’t even lend out my scan tool to colleagues or other tradesmen who work on our premises
The only tool I think may be appropriate to lend out . . . and only for worthy customers . . . is one of those devices which plugs in to the DLC and lights up when all the readiness monitors have ran to completion
Personally, I’d be ashamed to ask for such a thing, particularly since one can buy an OBDC scanner from Amazon for $20.00.
What model is this $20 item? Is it safe to keep this plugged in while I drive?
A 0.48 second google search code scanner gave me a ton of results… This was the 1st one in line … And no I have never used this model, but you get what you pay for…
Reread Dave’s post: Oops, maybe Nevada’s post!
Did you ever change the spark plugs and coils?? You never did post any codes, check them and post them here…
Nevada posted this…
16-01-003-1 Hyundai Technical Service Bulletin (tsbsearch.com)
As far as code readers, yes you can leave it plug in, mine displays on my cell phone.
Yes its safe. This is one i have.
Limited-time deal: ANCEL AD310 Classic Enhanced Universal OBD II Scanner Car Engine Fault Code Reader CAN Diagnostic Scan Tool-Black https://a.co/d/cQaVBlU
The problem is definately plug/wires/coils. I first replaced them (bad coil ) on my V6 Hyundai around 90,000 and a few weeks ago replaced them all again at about 140,000 miles.
The car didn’t store a code that could be read from my cheapo scanner but came up with the message “misfire on cyl 5”
The good news for you is that if you have the typical 4 cyl Hyundai, the parts are relatively inexpensive, access is easy and assuming you have the basic tools (Socket wrench set, screwdriver set and a $10 Harbor Freight torque wrench) pretty easy to do.
You sound awfully sure of that diagnosis 
Althoiugh admittedly it could be something else, such as a failing injector which actually does throw a code or something internal, having been through the drill twice already I think it’s a pretty good guess. Same symptoms, same lack of specific information, same lack of consistent fault and same level of frustration. 
Although I don’t believe in throwing parts/money at a problem, I’ve come to accept that at about 75,000 miles and the first signs of a misfire, replacing all the plugs, wires, coils and injectors is just faily quick, easy, inexpensive regular maintenance because if one component is starting to go probably another one isn’t far behind.
