It appears as though the ASPNET5 server code gen doesn't preserve the Swagger specified case for models. Specifically, the code gen will always PascalCase all model properties, instead of keeping the "on the wire" original definition.
Version swagger-codegen-2.2.0
Command line used for generation
java -jar modules/swagger-codegen-cli/target/swagger-codegen-cli.jar generate -i http://petstore.swagger.io/v2/swagger.json -l aspnet5 -o samples/server/
petstore/aspnet5
Related issues
Similar to issue #1926 for Typescript.
Suggest a Fix
A suggested fix is to include the [JsonProperty(PropertyName="{{baseName}}"] in the model template definition for ASPNET5. Alternatively the [DataMember] attribute could be used, as is done in the C# client definition.
Will submit a PR.