Sometimes you need to skip execution of part of a method under certain non-critical error conditions. You can use exceptions for that, but exceptions generally are not
I think people aren't being honest here.
If I, as your team lead, would see code like this you'd be up for a little one on one, and flagged as a potential problem for the team as that piece of code is particularly horrid.
I say you should listen to your colleagues and rewrite it following any of the suggestions posted here.