I have seen other flying eagle cents that have United States of America around the eagle but not the stars. And on the obverse it has United States of America around the reef.
I should preface this answer by noting that I am by no means an expert in early American coinage (I'd be far more comfortable discussing contemporary British coinage). However, with that caveat ...
There were a number of patterns produced prior to the official issue of the flying eagle cent. The process of preparation and design that led up to the issue is briefly described in the Wikipedia article on the Flying Eagle Cent.
The 1854 and 1855 patterns had an obverse similar to that in your example. An example of the 1854 pattern is included on the Wikipedia page:
Similar designs were used on the obverse of patterns produced in 1855, and some of these are shown on the CoinHelp site.
Importantly, it seems that the design of the eagle surrounded by 13 stars wasn't used after 1855. Further, as noted by Pieter Geerkens in the comments, the stars on the patterns of 1854 and 1855 do seem to be rather different from those shown in your example.
A Google image search found the "coin" in question on the Bonanza online marketplace site. The sellers other items include examples of Flying Eagle cents from 1854 to 1858. These are all listed at prices much lower than I would expect to see for genuine coins.
For that reason, I suspect that this example is actually from a modern set of Chinese "copies" based on the early patterns produced in 1854 and 1855. [Sets of these copies are pretty inexpensive online on sites like AliExpress.
The reverse of these copies have the legend United States of America around the wreath as you describe: