I'm going to respectfully disagree with you about this. Your free diving analogy is somewhat different. You're looking at holding your breath for a short period of time and returning to the surface. Equipment failure's do not come into play with that scenario. Entaglement hazards can happen and are a risk.
The "big issues" with scuba can certainly happen at that depth, and some more so. I don't know as though there's a certain depth that "big issues" are prone to happen in. Entaglement hazards increase substantially in shallow water, especially from a shore dive as presumably people could be fishing there. There is still the risk of equipment failure, as that's not depth dependant generally. You can get bent in a swimming pool, and you can get a pneumothorax (collapsed lung) in 6 ft of water.
While navigation isn't as much an issue, it still can't be neglected. Twenty feet of water isn't any safer than 100 ft of water in my opinion.
As to your issue with your girlfriend, like other's have mentioned...how much do you value her feelings? I'm fortunate, my fiance dives with me. But we've also made a deal that overhead environment's are off limits. I want to do them, she's adamently against it. It's a trade off and a comprimise. Since we're getting married in a few short weeks, her feelings and concerns are a concern to me. I'm still working on her to one day let me get into some virtual overhead stuff like deco diving. But that's still very much up in the air. And the bottom line is that if she say's "no," then the answer's going to be no and I'm going to have to live with it. She's not being unreasonable and saying I can't dive.
Only you can make your own decisions of what to do. But 20 dives really isn't much for experience, especially when you consider that the OW checkout dives are 25% of that number. To quote others, "YMMV."
Shane