Similar to what Christopher is saying:
Phlox isn't human. He isn't a Western Human living in the 21st century. He admits he didn't take The Hippocratic Oath. Just look at it from that point of view: a Denobulan convinced a Human Captain to make a horrible decision.
My problem with the ep is meta: This could have been our big 'source of the PD ep'...but it wasn't. They could have said the 'inferior race' were slaves (wern't they kind of? I don't remember the ep even touching on that) and made that the source of the drama. They could have said "Whoa whoa whoa...2 days is wayyyyy too short a time for us to come rushing in here and deciding the fate of billions"
Instead they...did what they did..and alienated (obviously) a great deal of the fanbase re the ep.