Umbraco-CMS: GetApplicationTrees throws exception after updating to MVC/Web API 5.2.7

Microsoft just released a minor update for MVC 5 and Web API, but after updating from (NuGet version) 5.2.6 to 5.2.7, the following exception occurs when requesting GET /umbraco/backoffice/UmbracoTrees/ApplicationTree/GetApplicationTrees?application=content&tree=&isDialog=false, making the back-office unusable:

Unhandled controller exception occurred System.Web.Http.HttpResponseException: Processing of the HTTP request resulted in an exception. Please see the HTTP response returned by the 'Response' property of this exception for details.
 at System.Web.Http.ModelBinding.FormatterParameterBinding.ReadContentAsync(HttpRequestMessage request, Type type, IEnumerable`1 formatters, IFormatterLogger formatterLogger, CancellationToken cancellationToken)
 at System.Web.Http.ModelBinding.FormatterParameterBinding.ReadContentAsync(HttpRequestMessage request, Type type, IEnumerable`1 formatters, IFormatterLogger formatterLogger)
...

The request itself returns a 415 Unsupported Media Type with the following payload:

)]}',
{"Message":"The request contains an entity body but no Content-Type header. The inferred media type 'application/octet-stream' is not supported for this resource.","ExceptionMessage":"No MediaTypeFormatter is available to read an object of type 'FormDataCollection' from content with media type 'application/octet-stream'.","ExceptionType":"System.Net.Http.UnsupportedMediaTypeException","StackTrace":"   at System.Net.Http.HttpContentExtensions.ReadAsAsync[T](HttpContent content, Type type, IEnumerable`1 formatters, IFormatterLogger formatterLogger, CancellationToken cancellationToken)\r\n   at System.Web.Http.ModelBinding.FormatterParameterBinding.ReadContentAsync(HttpRequestMessage request, Type type, IEnumerable`1 formatters, IFormatterLogger formatterLogger, CancellationToken cancellationToken)"}

It’s probably also worth noting the Microsoft.AspNet.Cors package is also installed and it only occurs only when the Microsoft.AspNet.WebApi.WebHost package (including dependent Microsoft.AspNet.WebApi) is updated to 5.2.7. Updating all other Microsoft.AspNet.WebApi.* packages to 5.2.7 does not introduce this exception. So there’s probably some change in these 2 packages that causes this exception…

Reproduction

Specifics

• Umbraco 7.12.4
• GET /umbraco/backoffice/UmbracoTrees/ApplicationTree/GetApplicationTrees

Steps to reproduce

Update the Microsoft.AspNet.WebApi.WebHost package to 5.2.7.