My understanding so that the height reached is one of the much more speculative pieces. It's based off the plane pinging a satellite and could easily be off several thousand feet. (Read that earlier)
No I think the height was from the radar, the part you are talking about is the ping reported a drop of 40,000ft in the span of a minute, which didn't make any sense.
The height of 45K is estimated with fairly large error bands. That aircraft couldn't get to 45K with the cargo and fuel it had at the time of the report.