Differing user-defined type guard and 'typeof' type guard behaviour when narrowing 'any'

In the below code, using a typeof type guard and an equivalent (I thought) user-defined guard, only one error is produced.

var y: any;

// Built-in type guard
if (typeof y === "string") {
    y.hello = true; // Correct error - 'hello' does not exist on type string
}

// Equivalent user-defined type guard
function f(x: any): x is string {
    return typeof x === "string";
}

if (f(y)) {
    y.hello = true; // No error with user-defined guard
}

Playground demo. Looks like user-defined type guards won't narrow from any, in any circumstances, as far as I can tell.

Start with the TypeScript Playground example in the issue and reproduce the differing diagnostics for the built-in and user-defined guards. Trace the compiler's narrowing behavior for an any value and verify that the user-defined guard produces the same error for y.hello as the typeof guard.