Borrow checking false positive on inferred closure type and borrowed fields

The minimal example constructed so far:

#[derive(Default)]
struct A {
    a: Vec<u32>,
    b: Vec<u32>,
}
fn main() {
    let mut a = A::default();
    let f = if true {
        |_v| vec![]
    } else {
        |_v: &Vec<u32>| vec![0_u32]
    };
    let u = f(&a.a);
    a.a = u;
    f(&a.b);
}

(Playground)

Errors:

   Compiling playground v0.0.1 (/playground)
error[E0506]: cannot assign to `a.a` because it is borrowed
  --> src/main.rs:14:5
   |
13 |     let u = f(&a.a);
   |               ---- `a.a` is borrowed here
14 |     a.a = u;
   |     ^^^ `a.a` is assigned to here but it was already borrowed
15 |     f(&a.b);
   |     - borrow later used here

For more information about this error, try `rustc --explain E0506`.
error: could not compile `playground` (bin "playground") due to 1 previous error

while the following modifications wouldn't anger the borrow checker and compiles:

• Using Vec directly: let a = vec![]
• Removing if: let f = |v: &Vec<u32>| vec![0_u32]
• Fully annotating the types: if true { |_v: &Vec<u32>| ...
• Removing f(&a.b)

Reproduce the minimal example in src/main.rs, starting with the inferred closure type and the borrow of a.a. Compare it with the listed compiling modifications, then verify that the original example no longer reports E0506 while the later call using a.b remains valid.