One possibility (JMO) is if, upon returning to Florida with the van and without Gabby, his parents hired the attorney who advised him to voluntarily check into a psychiatric treatment facility. If he voluntarily admitted himself, he has the right to walk out at any time.
In most states, adult psychiatric patients have the freedom to leave at any time (or, if hospital staff believes the patient to be suicidal, after the [typical] mandatory 48-hour observational holding period) and in some states those rights extend to children as young as 13. I know this because when I was 13, I was institutionalized for a month in a state where I was considered of the age of maturity after attempting suicide and I wanted to leave, so my parents transferred me to a facility in a neighboring state where the age of maturity was 18 for mental health treatment so I couldn't leave. I suspect without a court order keeping him there, BL might have very well seen the media coverage, freaked out, and took off.