Here is what the CP Database says about 'Big Mouth'.If your plant fits the registered description for 'Big Mouth', then its a Big Mouth.
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N: $[Dionaea ' Big Mouth ' {T.Camilleri}]
P: Carniv.Pl.:16 (1998)
S: =[Dionaea muscipula {Soland. ex Ellis}]
HC: name not registered with IRA, description insufficient
B: ?, before 1998
Nominant: T.Camilleri, 1998
Description: Carniv.Pl.:16
"A comparison of a conventional sized trap and the [Dionaea ' Big Mouth ' {T.Camilleri}] variety (sic!) which produces large traps on very short leaves."
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Unfortunately, I have not seen the original article [Carniv.Pl.:16 (1998)] that describes the plant, but if the quote from the database is complete, then virtually any VFT with "large traps on very short leaves" would fit the description -- whether green, red, or blue.