Yes.

There are no limits* to how high a pixie may fly, provided that they end their turn only one square above the ground. However, if they do end their turn above their altitude limit they fall with the consequences laid out for falling (1d10 damage/10 foot of drop).

*The theoretical maximum height a pixie may reach on their turn (with no extra movement trickery) is 8*3 + 1 or 25 squares high (run 8, trade standard for another run 8, action point for another run 8, +1 for starting height), that's 125 ft at the end of which they would fall. Falling says to subtract the creature's fly speed so that leaves us at 95 feet of fall, meaning 9d10 falling damage.

Your interpretation is correct

When the haste spell ends, the target cannot move. This counts as being "otherwise deprived of the ability to move" for the sake of remaining aloft. The creature would therefore begin to fall unless it has the ability to hover.

I researched this part of the rules when writing this related answer and there are no "subtle nuance[s]" or hidden rules. Remember that spells only do what they say they do and there are no hidden rules. If the rules for haste intended to give you some protection against falling it would say so.