Have I found two separate modules with ...errors around GD::Image

You have.

For GD::Tiler::tile to return an object as doco claims, it should return $tiled. I guess (untested) you could pass Format => 'gd' to avoid png, but return value would be GD image data in scalar, not an object.

With PDF::API2, it looks like plain bug in code; it should be method call (on $self) line #2241, compare to similar calls a few lines further (for jpeg, etc.).