Except when it isn't. Blessed types can overload operators - and then it's the type of the operand(s) that determine what's going to happen.

That's true. Since Perl is a quite mutable language, you can always shoot yourself and other in the foot with modules.

the symbol determines the operation, not the type

Except when it doesn't.

Sure, there are unfortunate exceptions. As far as I can tell they have been removed in Perl 6.