There's nothing stopping you from declaring additional static classes inside a class in Java. You can definitely declare multiple classes in a single file.
That's not even close to the same thing. C# allows declaration of types within other types, but it also allows declaration of multiple top-level types within a single compilation unit. And with partial classes, it also allows declaration of a single type across multiple compilation units.
It's a small thing, but between this and the properties syntax sugar (avoiding having to hand-write all the SetX GetX methods that litter Java code), it adds up for cruddy stuff where you end up needing to define a bunch of POCOs, for instance with EF or JSON REST APIs.
The point that was made is that multiple (static) classes cannot be declared in the same file, which is 100% false. I'm not arguing that C# is functionally equivalent to Java. There was no mention of "compilation unit" or "partial classes", which are a completely different subject.
It doesn't matter whether the additional classes defined in the file are top level or not, they're still classes that can be used independently.
You are being disingenuous. "File" is layman-speak for "compilation unit", so it is not a "completely different subject". You cannot declare multiple top-level types in a single compilation unit in Java. Yes, you can create static types within another type. However, those are not top-level types; they are scoped within the type they are declared in.
Let's just put it this way. Would a Java programmer, by way of normal operation, implement a project with a few Java files, each of which contains a type with several static types internal to it, and where those internal static types are in fact the main types of the program? If they wouldn't, then there is no equivalency, because this is something you see in C# code bases all the time.