A five-percent owner of a 401(k) profit sharing plan turned 70 1/2 in December, 2003 and terminated his employment effective January 1, 2004. In connection with the termination, he elected to roll all of his plan funds out into an IRA. My understanding is that the RBD isn't until April 1, 2004. Can we allow the participant to roll all of his funds out (including what would be the RMD amount) or was the RMD obligation triggered?

you are correct about the RBD, however the April 1 date is simply a delay in the distribution. It doesn't change the fact that the minimum distribution is still required
for the 2003 year. therefore the money 'should' be distributed first. otherwise it constitutes an ineligble rollover.
In fact, recall that there is nothing to stop from making the distribution by 12/31/2003 to prevent receiving 2 large distributions in one calendar year. often advisable.

He would have to take 2004's minimum distribution first as well.

When does an RMD obligation arise in a given year? On the first day of the year?

I imagine that the rules of Treas. Reg. s. 1.401(a)(9)-7 will apply under these circumstances, right?

See also 1.402©-2, Q&A 7].

Regarding your other question, the RMD obligation arises in the year the individual reaches age 70 ½, i.e. from January 1- therefore, any distribution that occurs on January 1 or after is attributed to the RMD and therefore not rollover eligible. This is excluding distributed amounts in excess of the RMD amount. For instance, if the RMD is $5,000, and the participant receives a distribution for $8,000, then $3,000 is rollover eligible.