Angular - Type 'string' is not assignable to type 'boolean'

Angular 4.3.1
Angular CLI 1.2.3
Typescript 2.3.4

Component Typescript file:

public saveName: string;
public overwrite: boolean;

The following markup fails with Type 'string' is not assignable to type 'boolean' when I run ng build --prod

<span>{{!overwrite || saveName}}</span>

OR

<button *ngIf="!overwrite && saveName">Save</button>

However, it works fine with the following:

<span>{{saveName || !overwrite}}</span>
<span>{{overwrite || saveName}}</span>
<button *ngIf="saveName && !overwrite">Save</button>
<button *ngIf="overwrite && saveName">Save</button>

Why am I getting that error?
More specifically, why does that error only show up when I have a negated boolean come before a string?