The official line for not inviting him (and other, what would be, cognizant officials) was to eschew giving an air ‘enforcement’ to the summit. Ostensibly, all there were to work out themes and policies.
The real reason they weren’t there is because they have a sworn duty to uphold the law. And, in the high capacities in which they serve, are obligated to act in a lawful manner. My guess is that Obama did not want them to be confronted with what some might call conspiracy and collusion to violate existing laws.
You're talking about an 'air of legality'? An air of people who know the laws and are familiar with the issues? An 'air' of people who know what they're talking about? Is that what you're saying?
I don't see how having people present who know the facts and statistics of the issues would conflict with 'themes and policies'.
How do you come up with themes and policies if you don't have facts readily available?
I'm missing something here... it still doesn't make sense.