PUT in IIS 7.5 - Error 404

I've deployed a web site using IIS 7.5, no WebDav installed, that's attacked by a C# WebClient which is trying to upload a file using the PUT method and anonymous authentication (these are requirements).

I'm getting this:

ModuleName IIS Web Core
Notification 16
HttpStatus 404
HttpReason Not Found
HttpSubStatus 0
ErrorCode 2147942402
ConfigExceptionInfo
Notification MAP_REQUEST_HANDLER
ErrorCode The system cannot find the file specified. (0x80070002)

These are the handlers as specified in web.config:

<system.webServer>
        <handlers>
            <remove name="StaticFile" />
            <remove name="ExtensionlessUrlHandler-ISAPI-4.0_64bit" />
            <remove name="ExtensionlessUrlHandler-ISAPI-4.0_32bit" />
            <remove name="ExtensionlessUrlHandler-Integrated-4.0" />
            <add name="ExtensionlessUrlHandler-Integrated-4.0" path="*" verb="*" type="System.Web.Handlers.TransferRequestHandler" resourceType="Unspecified" requireAccess="Script" preCondition="integratedMode,runtimeVersionv4.0" />
            <add name="ExtensionlessUrlHandler-ISAPI-4.0_32bit" path="*." verb="GET,HEAD,POST,DEBUG" modules="IsapiModule" scriptProcessor="C:\Windows\Microsoft.NET\Framework\v4.0.30319\aspnet_isapi.dll" resourceType="Unspecified" requireAccess="Script" preCondition="classicMode,runtimeVersionv4.0,bitness32" responseBufferLimit="0" />
            <add name="ExtensionlessUrlHandler-ISAPI-4.0_64bit" path="*." verb="GET,HEAD,POST,DEBUG" modules="IsapiModule" scriptProcessor="C:\Windows\Microsoft.NET\Framework64\v4.0.30319\aspnet_isapi.dll" resourceType="Unspecified" requireAccess="Script" preCondition="classicMode,runtimeVersionv4.0,bitness64" responseBufferLimit="0" />
            <add name="StaticFile" path="*" verb="*" modules="StaticFileModule,DefaultDocumentModule,DirectoryListingModule" resourceType="Either" requireAccess="Read" />
        </handlers> (...)

I've tried searching for solutions, but mostly they go for uninstalling WebDav (which I don't even have) or adding PUT to ExtensionlessUrlHandler-Integrated-4.0 (which I did to no avail).