As spotted by CometRobot, the palm trees in the NES game showcase an uncanny resemblance to those in Sega's 16-bit epic.
Sonic launched in 1991, with Adventure Island III coming a year later – so it's very likely that one of Hudson's artists aped the design.
While the trees aren't 100% identical, they're close enough to make it fairly obvious one was inspired by the other.
The Adventure Island series is an offshoot of Sega's Wonder Boy franchise; the original game 1986 Adventure Island (known as Takahashi Meijin no Bōken Jima in Japan) is an adaptation of the arcade game Wonder Boy.
Perhaps this was a cheeky way of referencing the Sega connection?