Do you agree with this that some people say?

Cool question, I've done martial arts for a while, but when I first began or rather a couple of months I sparred against a MMA fighter who trained for about as long as I did. I won... But, do you really win in sparring? 

I won 4 bouts against him 2 standing and 2 in grappling. He never did beat me even after we both trained for years. We were friends btw.

He was 3-1 a few years later. When we sparred again, I guess he thought he could beat me. I beat him again only because I tricked him a lot while sparring. Side kicks do work btw.

If you don’t train full contact, a high level fighter that has competed full contact on numerous occasions will have a serious advantage. Even if you fight dirty, if the professional fighter (who is also likely a natural born elite athlete) can defend against your punches and kicks, they can also defend against your eye gouges and nut kicks because you still have to be able to land those shots like anything else.

If you are a high level martial artist who also has trained full contact, you might have a chance.

Well, it's just a fact that you are not allowed to gouge out eyeballs or rupture testicles in a MMA fight. 

No.

First, not everyone who knows how to fight and fight well are interested in competition or even notoriety. It may come as a shock to a mind of a child and the immature, but there are people who are very good at what they do because they love what they, and they don't care for fame, popularity, much less if anyone knows it.Second, MMS and UFC are not the only venues in the world for martial arts. There were such competitions long before MMA and UFC came into being and that is just counting the legit ones and not the underground tournaments.

It comes from the same mentality who think navy SEALs are the top elite in the world and they are not. FYI team 1 thru 4 are Spec Ops not SF.

It also come from same mental cases who think SEALs can ot be beat in hand to hand. Ad that is last thing on their mind and training.

You fight how you train. You train how you supposed to fight. It is cyclical that 1 part of the equation actually is part of the solution.

There is why most MMA fighters are terrible at certain things. It goes to their training and what they lack.

Personally i have beaten some of the best in the world at hand to hand (seriously not kidding) (it was down to him or me). And i had only my TMA and few things like this. And this was an individual trained in the military hand to hand. (L.I.N.E. training, initially he did have lot of TMA as well).

It nothing  like what MMA fighters do. Fighters fight, warriors lay waste to the enemy. MMA is a fighter mentality. And that is their stumbling block and thought process. It goes down to how you train and what you train.

If one has zero training - Very unlikely they would win without extra help (e.g. weapons, another person, element of surprise). 

With TMA or single martial art/non hybrid combat sport training - Depends on a number of things. Being a pro doesn't necessarily mean someone is head and shoulders above everyone else. UFC, PFL, Bellator, and the like are of course the highest echelon of MMA competition. So one could argue in most cases a fighter of that caliber would win. But there are plenty of "Toughman" competition-level fighters out there that are only a step above an undisciplined street fighter. An experienced TMA practitioner could absolutely devastate someone at that level. Many MMA fighters don't specialize in any one thing. So while it is great to be well-rounded a lot of them have serious holes in their game capable of being exposed by someone able to impose their strength (i.e. one facet of the game). 

 Lots of TMAs have competitive formats that are on par with pro leagues too. I'm all for people feeling MMA competition is the highest level of combat sport competition. But it doesn't mean MMA fighters are the greatest at everything. A well-rounded person has an advantage with less rules. But they can still be exposed if there's a huge gap in skill. There's no way an MMA fighter is just going to run through a Judo or Sambo master. They can still get knocked out by a good kickboxer or boxer too. It really depends on a number of things. 

There is always somone better no matter who you are and in all things.

To the average Joe then yes. However an elite martial artist or boxer has a shot against an MMA fighter. It depends on the environment and the area the MMA fighter specialises in. An MMA fighter who is great on the ground but poor in stand up would be useless against a boxer in a street fight where it's hard or damaging to get them on the floor.

Depends on the circumstances.