Behavior of Iterated 3-DES
Yes, It is what you understood. You use the same key for each encryption.

If you think that they used different keys for each TDES (3DES) they need to store one million keys. This is not practical for the attacker but also for them. 

It can also be written as $c = \operatorname{TDES}^{(1000000)}_k(m)$

The point in the section distinguishing these iterated from a random permutation and possible attacks that can be faster than brute-force.