It sounds very reasonable. They've updated the app in a major way about twice in the past few years. The problem I have is that there hasn't been an update since I got my new phone, and the old one was running 4.4.2, and the app still worked. I know it was working, because a few deposits went in - and I made them with the phone. (But that was on a Note 3, and it had a lot more than an S3. It's possible that the new update just won't run in a 1GB space.)
I'd try clearing the app cache (in Settings/Storage), then starting in recovery (Volume Down/Home/Power) and clearing the system cache - don't clear the system data - then restarting the phone, installing the app (I assume that you've uninstalled it already - if not, uninstall it before starting any of this) and see if it works. If not, you're in the position I was before I bought my Note 3 - buy a newer phone or don't use your phone for the bank. (You can still pay your bills and check your balance on a PC, or even on a web page on the phone, but you'll have to go in to deposit checks.) But remember, the S3 is going on 6 years old. There are a lot of things that won't work in it - probably Walmart Pay, definitely Samsung Pay or Google Pay, etc. (And any app that needs more than 1GB of RAM - and we'll be seeing more and more of them as the "smaller" phones come out with 2 or 3 GB of RAM. It's usually due to sloppy programming, but it happens.)
I really doubt that the problem is the security requirements - I'm not even asked for my unlock code when I run the app - let alone a fingerprint. (But the customer service department of PNC isn't filled with software developers, all they know is what they're told to say.)