I have a commercial app that has a completely legitimate reason to see the SSID of the network it is connected to: If it is connected to a Adhoc network for a 3rd party hardware device it needs to be functioning in a different manner than if it is connected to the internet.

Everything I've seen about getting the SSID tells me I have to use Apple80211, which I understand is a private library. I also read that if I use a private library Apple will not approve the app.

Am I stuck between an Apple and a hard place, or is there something I'm missing here?

As of iOS 7 or 8, you can do this (need Entitlement for iOS 12+ as shown below):

@import SystemConfiguration.CaptiveNetwork;

/** Returns first non-empty SSID network info dictionary.
 *  @see CNCopyCurrentNetworkInfo */
- (NSDictionary *)fetchSSIDInfo {
    NSArray *interfaceNames = CFBridgingRelease(CNCopySupportedInterfaces());
    NSLog(@"%s: Supported interfaces: %@", __func__, interfaceNames);

    NSDictionary *SSIDInfo;
    for (NSString *interfaceName in interfaceNames) {
        SSIDInfo = CFBridgingRelease(
            CNCopyCurrentNetworkInfo((__bridge CFStringRef)interfaceName));
        NSLog(@"%s: %@ => %@", __func__, interfaceName, SSIDInfo);

        BOOL isNotEmpty = (SSIDInfo.count > 0);
        if (isNotEmpty) {
            break;
        }
    }
    return SSIDInfo;
}

Example output:

2011-03-04 15:32:00.669 ShowSSID[4857:307] -[ShowSSIDAppDelegate fetchSSIDInfo]: Supported interfaces: (
    en0
)
2011-03-04 15:32:00.693 ShowSSID[4857:307] -[ShowSSIDAppDelegate fetchSSIDInfo]: en0 => {
    BSSID = "ca:fe:ca:fe:ca:fe";
    SSID = XXXX;
    SSIDDATA = <01234567 01234567 01234567>;
}

Note that no ifs are supported on the simulator. Test on your device.

iOS 12

You must enable access wifi info from capabilities.

Important To use this function in iOS 12 and later, enable the Access WiFi Information capability for your app in Xcode. When you enable this capability, Xcode automatically adds the Access WiFi Information entitlement to your entitlements file and App ID. Documentation link

Swift 4.2

func getConnectedWifiInfo() -> [AnyHashable: Any]? {

    if let ifs = CFBridgingRetain( CNCopySupportedInterfaces()) as? [String],
        let ifName = ifs.first as CFString?,
        let info = CFBridgingRetain( CNCopyCurrentNetworkInfo((ifName))) as? [AnyHashable: Any] {

        return info
    }
    return nil

}