In order to save the President, our heroes or their underlings have to defeat the very measures in place to protect the President. On the other hand, the people in charge of the measures are hoping to see the President die. All sorts of funny things can happen in a race where both sides desperately want to lose...
Beaming down at or anywhere near the conference should be impossible - but Cartwright would want to make it possible for his assassin to beam out, after being spotted and mistaken for a Klingon, but before being captured or killed and exposed for a human. So Kirk and pals could beam down, either because Cartwright left a permanent hole in the defenses, or because Valeris gave them the means to get Cartwright's folks to open a hole for them.
Why not send redshirts, though? Well, given the rate things were going, any one of them could have walked to the President, said "Captain Kirk sent me - there is a threat to your person, Sir", and blown his head off. Kirk could trust himself, sort of trust McCoy and Spock, and had little hope left if he couldn't trust Scotty, Uhura and Chekov. He could always send the redshirts to stop Cartwright's troops elsewhere in the compound.
Incidentally, given how much Valeris knew of the overall cabal, it should be logical to assume she knew some key details of the assassination plan, such as "assassin will be perched behind this window here" and "this code will open the shields to transport" - necessary details for our heroes to achieve what they did. But given this, we must also assume that Valeris perfectly well knew the location of the conference, and that Spock accepted her lie solely because he felt he could and should not dig out the truth, not with the methods at his disposal.
Timo Saloniemi