Everyone seems to have this same question. The answer linked is correct as far as I know. You are not forced to qualify/certify your Bluetooth device under the Bluetooth SIG, but if you don't then you're not licensed to use the Bluetooth trademark.
"The Bluetooth SIG does not force members to use the trademark on products incorporating Bluetooth technology, but if the trademark is used then it can ONLY be used by a member of the Bluetooth SIG and for a properly declared product."
There seems to be conflicting information scattered about on the web but we couldn't find anywhere where Bluetooth SIG says you have to qualify the product.
"If I don't put the Bluetooth logo on my product, do I still need to list my product with Bluetooth SIG?
Yes. In all products that incorporate Bluetooth IP must adhere to the Bluetooth Compliance Program. Details on this program can be found on the Bluetooth SIG site."
I'm not sure how accurate TI's answer here is. More than likely they just want Bluetooth SIG to get the money. The chip, subsystem, PHY, stack, etc. has already been qualified/certified.
Compliance Enforcement -- I did ask "what if I don't use a trademark, nor mention Bluetooth is being used" Never got a response.
I personally know someone with a product on the market where he simply does not market it as being a Bluetooth device.
What if the logo isn't used in marketing materials except for textual mentions, e.g., "Technical requirements: Bluetooth 4.0 enabled phone"?
The compliance enforcement does mention using the word "Bluetooth" as being a part of the trademark. "The Bluetooth® trademarks—logos and the word "Bluetooth"—are owned by the Bluetooth SIG." Source: https://www.bluetooth.org/en-us/test-qualification/qualification-overview/qualification-enforcement-program
However, I don't think the acronym BLE is trademarked, they dropped Bluetooth Low Energy in favor of "Bluetooth Smart", so you could probably get away with using "BLE", which everyone associates with Bluetooth 4.0.