"I recently had a conversation a gentleman at $BANK who told me that their mobile banking app was more secure than online banking with a desktop PC."
That's ok. I don't use a PC online (I have a Mac). Aside from that, I don't do banking online at all anyway.
The thing I run into frequently is when I call customer service somewhere and they've identified me from caller ID. If someone nicks my phone or spoofs the number, they can get in at many places. I also don't like it when the ask to "verify" some information. The problem is they don't understand the word "verify" and I don't want to volunteer information over the phone. It wasn't that long ago there was a story on Rip Off Britain or some such show where they told of a guy that got a job at a bank and was passing on people's security information via text to some accomplices when he spotted nicely stuffed accounts. He was something of an idiot but the people paying him for the info weren't and they hadn't been collared in a year's investigation.