Is this the engine or the transmission?

About a week ago I had the oil changed on my 2014 Ford escape at the dealership. Everything seemed fine at first.

The car seemed loud for about 3-5 days but I didn't think anything of it because it was driving great Sunday the 10th I drove from my home to about 5 miles away. It was fine but loud on the way home things started to go very poorly losing power odd shifting and just general odd behavior I was very low on gas so I pulled over into the gas station and gassed up I made it about 10 feet and it died. You can see I pushed the vehicle from the spot it was stuck in back and there was oil everywhere all over the ground. There was also a burning smell.

I had to get a friend come help me and we pushed the vehicle into the spot.

The car only has 28k miles on it. When I first had the car in for its very first oil change at the dealership, they forgot to tighten the oil filter, and all the oil leaked out causing the engine to seize. It seems like the exact same thing has happened again, but the dealership is claiming this is a transmission problem, and completely unrelated to the fact that I had an oil change last week. Its under warranty, so they are fixing it. But I feel like they are being dishonest. Can anyone give me an opinion on what this might be?

They killed your engine and don't want to admit it. Document everything, take pictures of the mess if it's not too late. They may be playing some kind of game with Ford so they can get reimbursed for the engine by claiming a transmission. Personally I would be pretty angry and wouldn't let them near the car until it was clear on paper what happened and what was being done to get me a brand new engine only.
Probably a good idea to phone Ford customer service and have a zone rep come down and have a look at the situation.

Oh we all have opinions. You send a picture and a story of no use and then you want a opinion of the trustworthiness of the dealer. Looks like you have your opinion set in stone, so what what we think. Since you suspect the same thing has happened again did you think to check the engine oil level? No, I didn't think so.

It doesn't really matter what it is, they are fixing it.

*** Update***

No indicator lights came on at all. The first time this happened with the dealership the check engine light did come on. Thats the only difference. No I did not check the dipstick, as I called the dealership to have them come and tow it. I can't say for sure the color of the oil, as it was raining. But there was a lot of it, in my opinion it was more on the brown side, but it was raining. I trusted them to figure out what was wrong and take responsibility for it. I realize it is all under warranty, but they are just claiming this to be a transmission issue etc. OK, maybe it is. I guess its really bad luck to have a transmission go out on a 2 year old car, that has every service update possible. And, I get all the service done through the dealership.

The reason I'm questioning the honesty is because I have one year left on this lease, and I was requesting to them that I can get out of it and into a different vehicle. I have zero confidence in this car anymore. Thankfully this didn't happen on the highway with my kids. (Which is what happened the first time.) I have already paid off the final year of the lease, and they are now stating that there really isn't anything they can do. It is just frustrating, as I simply want a reliable vehicle. I suppose it isn't the end of the world since it will continue to be under warranty for the remainder of the lease.

Let them keep fixing it and turn it in at the end of the lease. The motor should not be noisy but it sounds like the trans is bad. Speak with the service manager in his office and also the general manager to make you happy so you will buy another car.

Seems a little light weight for engine oil with that iridescence, looks more like transmission fluid.
Check your receipt from the oil change and see if they checked or changed the transmission filter.