It looks like it's a bug with Chrome.
You can see the difference by adding the below CSS on input field.
input:invalid {
color: blue;
}
When you reset on FF, the input field becomes invalid but on Chrome, it does not. On Chrome, if you select a file and then bring up the select screen again then cancel it, the field becomes invalid. That seems like the only way to reset the input field.
Looks like you will have to add some code.