I agree with the fact that Lupin most likely just under went a transformation due to a full moon. The reason is this after the Summer Soltice in June the remaining full moons of the year fall somewhere after 15th of each month with August normally beening the lastest. This year's August full moon falls on the 29th.
Lupin didn't choose to be in the compartment with the trio, they choose to be in the compartment with him. Why? They were late getting to train from the Leaky Cauldron and the other students had avoided the compartment as if it had the plague. No other students wanted to have they last bit of freedom interferred with but the trio had no other choice because the other compartments were filled.
This is noted on page 74 of POA: Quote:
Harry, Ron and Hermione set off down the corridor, looking,for an empty compartment, but all were full except for the one at the end of the train.
Additional thought: If Lupin had just transformed it might have been without the Wolfsbane Potion. If so, the transformation would have been that much more difficult for him. He told Harry when they spoke about the potion was a recent discovery, and he wasn't a very good potion maker that is why Snape brewed the potion for him. It was a complex potion.