So I ran across a forgotten weapons video and the dude said that MP5s were intended to be shot in semi and FA is only used for when things go south, (more or less).

Is that really the case?

No. That’s dumb.

Yes - It was "intended" this way.  However use has expanded way beyond foreseen expectations.  Often the doctrine of use determines that accurate shooting (e.g. semi-auto) equates to better hit placement, less stray rounds and this tends to be a model used widely.

When it emerged, it was a closed bolt SMG almost a handy carbine capable of accurate shooting.  Looking at its contemporaries of the day (Uzi, Sterling, MACs, PM12, etc.) subguns were capable of some accurate shooting but not like being able to shoot as precisely as a carbine.  The tactics for SMGs were often holding at waste level and bursts (bullet hoses for suppressing volume of fire).  Not really sure why the M2 Carbine wasn't well utilized in the SMG role after WW2, but I'm no expert either.

Enter in the MP5 with its ability to hit a target as easily as a 22 rifle placing accurate hits when you want it to and more controllable full auto fire.  The natural advantage it had over its contemporaries was semi-auto accurate fire = shoot a guy in the head or other accurate-ish shooting at 50 yds.  Can't do that with an open bolt sterling very easily.  It can be done, but not as easily.

This, and to add I'm guessing the statement the OP saw was centered more around the fact that the MP5 is a closed bolt SMG.

Most SMGs of the WW2 era and even beyond were open bolt designs for simplicity.  A lot of open bolt SMGs are full auto only, and even those that do have a disconnector to fire in semi-auto, it can sometimes be hard to get good precise shots on open bolt guns because pulling the trigger releases the bolt to slam forward, which is a lot of moving mass in a blowback gun that can cause the gun to move around a bit in your hand between the moment you pull the trigger and the time the bolt slams home on a round and fires.  Closed bolt designs just have the movement of a striker of swinging hammer, which is easier to hold steady during the lock-time.

So that, plus the ergonomics of the gun and the design of the sights show it was designed with a priority to good accurate shooting, for an SMG at least.

Reading from Frank James' out of print "Heckler & Koch's 9Mm Mp5 Submachine Gun", HK training doctrine was two rounds.  I'm assuming this was in semi?  I know from shooting mine, I'm usually on for 2 rounds.  By the third round, I'm stating to drift.  Again in semi.

And I believe the FBI's trigger pack was safe or semi, no auto?

But I've never been to any official HK MP5 training, so have no idea what's being taught.

I recommend the above book for anyone interested in the platform.  I bought mine years ago when they were cheap, but expect to pay $100+ for these today.  I saw used ones at Amazon starting at $140.

It was, but the safe/semi/auto MP5 was around for decades before then.

Sort of.  I'd learned from an Hk training graduate that the unusual 0-1-2 lower was a request by UK SAS/SBS because they intended aimed headshots with two 125gr rounds causing twin wound channels a few centimeters apart on a moving target.  That's 250gr combined to cause an overlapping wound that's like blowing a golf ball sized tunnel straight through a fleshy target.

They regarded 2-round burst as a perfect method and that it'd take anyone down.  Single shot usually would, but double shot always worked.  Plus it regulates a 30-round mag into an acceptably regulated 15-round mag.

FBI stands pat on one round.

Wow.  So binary triggers aren't so gay after all...

Don't worry, they are still gay.

Having owned the binary and shooting the real stuff, its simply no comparison.

FA MP5SD is what dreams are made of

Yes, the MP5SD is an amazing gun to shoot.  It can be a little bit finicky with regard to magazines and ammo.  It works best with full powered ammo and straight mags loaded to 28 rounds or less.

My favorite is the MP5K, especially suppressed.  It is very controllable and still accurate in full-auto or 3-round burst.  It will feed and cycle almost any ammo through any magazine without difficulty.

Yep.

Intended for Hammers, controlled pairs and failure drills.
I generally drill using triple taps and Bill Drills with the MP5 platform on semi.

Then again, it isn't hard to empty a 30 rd. mag on auto into a a fist sized, A zone group at 21 odd feet.