The EMH has got some nerve thinking that 1) he's the only doctor who's ever lost a patient, and 2) he's somehow "above" having to make decisions as to which patient should live and which should die. Every doctor in history has had to make decisions like that; the EMH isn't "better" just because he's a computer program. He deserved to be slapped because of that stupid ego trip he had.
That being said: Obviously the EMH wouldn't deliberately
let Jetal die, but maybe it was subconscious. In which case he's obviously not responsible. No one is ever responsible for a subconscious act - that's logically impossible.
And let's be frank: Anything that helps him make a decision, given two absolutely equal choices, is kind of a good thing. Either Harry dies, Jetal dies, or both die. The EMH was at a roadblock, so to speak: he couldn't decide. He was waffling about it, and something had to break that deadlock.
So maybe his friendship with Harry subconsciously influenced his decision. That may seem harsh, but if the alternative is that both Harry and Jetal die, it's better that only ONE of them die; anything that helps him make a decision as to who, even if it's totally 'automatic' and blameless, is better than nothing. Something
had to help the Doctor make a decision, so even if it was something arbitrary like this, that's better than the Doctor making no decision at all and letting both patients die.
The very fact that the Doctor felt guilty about it, is reason enough to let him off the hook. If he was as bad as he accused himself of being, he wouldn't have cared. He clearly did care, so he had the presence of mind to feel bad about it. That's entirely normal - sentient beings do that. It's part of what it means to be sentient.
On the other hand: Perhaps it wasn't the Doctor's friendship with Harry that (subconsciously) influenced him, but the fact that Harry was a bridge officer. Being one, Harry was - arguably - more valuable to the crew than Jetal was. Somebody should have pointed that out.