Basically, it seems that the Broadcom Bluetooth chipset within the 2012 Nexus 7 is Bluetooth 4.0 LE/Low Energy (BLE) capable, however, Google never certified it as such, only certifying to the then current v3.0 spec. This means that Google probably now see no financial benefit in re-certifying the device for legal BLE development (as the 2012 Nexus 7 is now EOL). However, there is a light at end of the tunnel.
Manuel Naranjo has created a Android Open Source Project (AOSP) code patch (which I believe Google avoided, due to the above) which he has submitted, freely, to the AOSP-based CyanogenMod project (specifically in versions 10.2 and 11 based on Android 4.3 and 4.4 (KitKat), respectively). This means that we do get BLE for the 2012 Nexus 7 (codename 'grouper'), if you install CyanogenMod (or possibly Purity Rom).
If you're interested in the BLE patches Manuel made, they can be found here, his changes are reasonably easy to follow (he removed the 'false' switches for BLE etc., amongst other changes).
I would assume that these patches could also be applied to the stock 2012 Nexus 7 Wifi ('grouper') Google Android source build (which can be found here), if a 3rd-party custom Rom like CyanogenMod wasn't to your liking (Nexus 7-specific binary hardware drivers, required for the build, including Broadcom Bluetooth, are available here).
I'm looking at picking up an older Nexus 7, as they're very low-cost right now (£99 in the UK), and Google/CyanogenMod will probably ensure a continued upgrade path, for some while (I'm hoping for BLE Peripheral support, possibly in Android 4.5).
BTW, Manuel also markets a Nexus BLE Helper @ Google Play (paid) which I assume somehow simplifies the installation of his workaround, without have to flash the entire OS. (Disclaimer - I am no way connected to the developer).
Edit: I found this additional thread which pinpoints the Bluetooth omission within the Google codebase.