This is generally the same experience I have had. I'll even talk through the assumptions (e.g. "Can we assume I know how to do argument checking?") and then after I've done the heavy-lifting of the problem-solving I'm now discussing how I didn't do something I brought up as an assumption.
Also, generally, if I'm whiteboarding in front of my coworkers/team/etc. I'm discussing something I've thought about for more than the few moments I have to digest the question while standing at the board during an interview.
Also, generally, if I'm whiteboarding in front of my coworkers/team/etc. I'm discussing something I've thought about for more than the few moments I have to digest the question while standing at the board during an interview.