Could the trailer's jack have been raised to not high-center on the railroad track?

Assuming you mean "landing gear." No way to tell from the video. Landing gear height can vary a bit even on new trailers. I can see the trailer tandems are all the way forward that "could" be a contributing factor depending on the grade of the road on the other side. Another possibility is fifth wheel position. If it was all the way to the rear it could allow the gear to catch easier.

 

This happens fairly commonly (landing gear pads hang on high, raised grade crossings) Happens mostly with heavy, loaded trailers but it can happen loaded or empty in the right situation and angle and approach.

In some situations, a driver will fail to crank them up all the way leaving them down maybe 2 inches lower then they should be (laziness) but I suspect this is rarely the case.

 

On the video there is quite an uphill slope on the trailer side of the crossing. More slope than usual.
What we don't see is the final position of the landing gear, to determine if it was cranked all the way up or not.
Landing gear height, even in the fully up positions, can vary from trailer to trailer.
But judging from the uphill grade, and the tracks being on a "high point", it would appear within reason for a trailer's landing gear to bottom out on this RR crossing, even if the landing gear was raised to it's fully upmost position.

 

Looking at the end of the video where I can see the pitch of the crossing, I'd say most drivers would have taken one look at that and not attempted to cross the tracks.

EDIT: I looked at this crossing in Google Maps. There's a 5 ton weight limit sign at the crossing. The article also said :

Can't fix stupid wins again!

 

He forgot to go into the menu/settings and check the railroad track hump detour box!

The first one to write the country song "You Can't Fix Stupid" will become rich!

 

I know when I look at the landing gear on my 07 TRANSCRAFT the Dolly's dont go up as much as I think they should

 

Being further forward actually elevates the nose of the trailer and lowers the tail; one reason some shippers want tandems slid to the rear, as to mate trailer to dock height.

 

This link to Operation Lifesaver, the educational arm of the American Railroad Association tells the story of how many RR crossing collisions there are:

http://oli.org/about-us/news/collisions-casulties

Although the number is decreasing, it is taking longer than I thought to clean out the gene pool.