The programme called America Unearthed investigated evidence that there was a cultural connection between the Maya and Creek Native American peoples. This was in the form of language, architecture, building styles, art and cultural practises. However the programme was obviously more interested in entertainment instead of fact.
The programme did constantly point out that the idea was being dismissed or even suppressed by the academic community (they were also apparently refused access to the archaeological site that has the most evidence by the government), but all "experts" that they had on said that yes, there was a connection in some form or another.
Does this theory have any actual truth behind it? Or is it as historically accurate as Ancient Aliens?
Dismissed not suppressed. Basically mass media is not familiar with most Native American peoples, such as those of precontact Texas and Northern Mexico, so they glom onto whatever tribes are well-known. Northwestern-most Maya settlements exist in Chiapas. Although not Muscogee Creek proper, the Natchez are some of the western a Muscogeean-language speaking people who lived near the border of Louisiana and Mississippi. Google maps provides a map of the distance, a trek of 2,562 km (1,592 miles). It's not impossible that someone would make this journey, but not particularly likely, but why would they skip over thousands of other peoples along the way?
As far as languages, Muskogean languages and Mayan languages both are separate primary language families. There is no known connection; however, a person could find coincidences between any languages in the world.
Towns organized around a central plaza are found throughout the world. It's just practical to build around a common meeting space and place governmental and religious buildings close-by. Monumental mounds are built by precontact Indians from the Amazon to Eastern Canada.
The connection between the two groups is the lifestyles around tobacco and maize cultivation, introduced from Mesoamerica to the southeast (and beyond. BTW maize is believed to actually have originated in western Mexico and tobacco possibly from the Amazon). These crops and their accompanying stories were passed from tribe to tribe. The model for ideas spreading across ethnic groups is cultural diffusion.
The Maya-Creek connection, especially as presented in "America Unearthed" is a pet theory promoted by Robert Richard Thornton, the Creek architect interviewed at the beginning. I discussed the basic history of Thornton's hypothesis here.
The hypothesis is mainly based on making overly optimistic connections between coincidences while ignoring deeper history. It's been too logn since I've seen it to make too many specific points but here are some general issues.
They mention the Mayaimi and the Mayaca in Florida at one point to suggest that they were linguistically related to the Maya. However they appear to actually be connected linguistically related to the Calusa, who in turn potentially have ties to the Tunica in the Mississippi Valley. In which case the "Maya-" portion of of their names don't have any relationship to the "Maya" but is derived from the Calusan "Mayai" -- "On the other side", a reference to them living on the far side of Lake Okeechobee. Sometimes languages just end up with names that have similar words. On a related note, Mayaimi gave English "Miami", but no one is suggesting they're closely related to the Miami (Myaamia) of Indiana and Ohio. Based on America Unearthed's logic though, you would.
As far as architecture and building styles, there's no real need to evoke Mesoamerican connections to explain Creek designs.There's a long and widespread history of monumental architecture through the region, going back to Poverty Point nearly 4000 years ago (and technically speaking even further back, but Poverty Point is the first that seems to combine monumental architecture with living space). Plenty of local inspiration that doesn't require Mayan intervention.
Or is it as historically accurate as Ancient Aliens?
America Unearthed is in the same vein as Ancient Aliens, a bunch of fringe theories trying to pass themselves off as the underdog against the oppressive forces of Big Archaeology. Of course, it's not as out-there as Ancient Aliens, but it still loves its ill-supported hypotheses.