This episode and its song is named after and a parody of the 1956 song of the same name by Elvis Presley.
The Amazing Place is a parody of two CBS shows; the name is a parody of The Amazing Race, and the concept of the show features elements from The Amazing Race and Survivor.
Elements from The Amazing Race include:
Teams (or in this case, couples) competing against each other, with the last place team eliminated after completing a stage;
Elements from Survivor include:
The setting of the show is on an island
The show references Robert "Boston Rob" Mariano, who competed on both Survivor and The Amazing Race.
Boston Rob first competed in Survivor: Marquesas and reappeared on Survivor: All-Stars, Survivor: Heroes vs. Villains, and Survivor: Redemption Island. During Survivor: All-Stars, he formed an alliance with Amber Brkich, which evolved into a romantic relationship; both made it to the Final Two during All-Stars, with Amber winning by a vote of 4-3; Boston Rob proposed to Amber prior to the final votes being revealed during the show's live finale.
As an engaged couple, Boston Rob and Amber competed on The Amazing Race 7, finishing in second place. They would get married soon after Amazing Race 7 aired, and reappeared as a married couple in the Amazing Race All-Stars in 2007, but were eliminated after the fourth leg.