The relative I know with a Lifelink-type cell phone was given a bottom-end Tracfone, one that costs $9.99 at Rite-Aid. There was no choice of phone, just fill in the application and that is what they sent.
The phones they send out are all re-conditioned phones that have been turned in. You are correct, there is no choice, you get what they send you. My aunt who is on SS applied for one and they sent her a smartphone.....nothing worked on it but the phone part. It was an obvious used Samsung, there were scratches all over it.