Generally agreed, but not quite with the bolded bit. Given the size of the universe, I think it's virtually impossible for there not to be intelligent alien life elsewhere (although given relativity, "this precise moment" is not really a meaningful concept when considering large distances).
What you say about relativity is true but if we put that aside for a moment and imagine that there is a "now" which extends throughout the whole universe. If we could be outside the universe, pause time at this precise second and then look at every single planet in the universe, would there be other intelligent life ("intelligent life" here being defined as life that has a comparable level of intelligence to ours or greater) in that "now"? I see no reason to suppose that there would be.
The way I look at it is this. Firstly, while for some species intelligence is a trait which facilitates survival, we've got enough stupid species which do perfectly well on this planet to make it perfectly clear that it's not necessary. Dinosaurs were thick as molasses and they ruled this planet for many times the length of time we've existed. Hell, bacteria have
always ruled this planet, and they certainly can't be said to be intelligent. Furthermore, there's no reason to suppose that there's any particular reason for favouring
our level of intelligence. We know that in this planet's history that it's only happened the once. So I don't think there's any reason to suppose that our level of intelligence is particularly likely to occur on any planet, even if it has a long history of thriving complex life.
Furthermore, our level of intelligence would seem to be something of a threat to long-term survival. We're still creatures of instinct and emotion. We evolved to see things in the short-term. We evolved as tribal, territorial and aggressive. These things have not changed, even though they are somewhat mitigated by our intelligence - but only somewhat. Furthermore, we've developed the ability to manipulate our environment in such a way as to be hazardous to ourselves. We have caused damage to our environment which will have repercussions for years to come (and are still doing very little to reverse it). We have weapons which could wipe out all life on this planet and it's not unthinkable that they could be used again one day (nuclear weapons have gone missing and still cannot be accounted for, North Korea has nuclear weapons, etc.). We are multiplying at a rate which, if left unchecked, will leave us unable to support our global population. And so on.
Again, all of these things are mitigated and it doesn't look likely that we're going to be wiped off the face of the Earth any time too soon, but who can say where we'll be in 100 years time? And who can say what position an extraterrestrial intelligence like ours could be in - what if their version of the Cuban Missile Crisis had gone a different way? I don't think it's unreasonable to say that our level of intelligence coupled with our inbuilt evolutionary traits (which I think it's not unreasonable to assume other species of our level of intelligence would possess, knowing what we know about intelligence and evolution) can be a danger to long-term survival for a species.
Then look at how short a time we've been around on this planet. Life has existed here for 3.8 billion years. Complex life has existed for 1 billion years. We've existed for 100,000 years. We've been around for 0.01% of the length of time that complex life has existed on this planet, and it's not unreasonable to say that we may be on the brink of extinction on a geological timescale. That's a tiny, tiny amount of time. Thousands of times smaller if you restrict it to when we've actually had technology of note, or much, much smaller still if restricted to our above-posited frozen "now".
For me, the chances that our possibly brief, brief span in this universe will coincide with the possibly equally brief, brief span of a comparable species takes the high probability of intelligent life existing somewhere at some time and turns it into a low probability of intelligent life existing somewhere
right now. I mean, I'm happy to admit that I could easily be wrong. This is all just conjecture upon conjecture based on such a tiny set of data (or, even, on just one datum) that there's no way we can even say what is or isn't probable with any degree of certainty. But that's the way that I see it.