I think you're both talking about retaliation missions. My point is about all other alien activities : AFAIK, alien missions are a sequence of UFO sightings in a region for a month, and if you stop one, the remainder are cancelled. If you want to see large UFOs with many power sources (ie Elerium), leave the small scouts fly.
You're correct in saying to leave the small scouts fly, but only if you don't want to delay the large UFOs from appearing.
As Meridian has stated, shooting down UFOs only delays the next UFO scheduled in the alien mission, up to 9 days, and never cancels them. This can really have an impact on certain missions like Alien Harvest, which have 9 UFOs assigned, since the mission can be delayed for several weeks or even months. This also applies to Retaliation missions: shoot down the scouts both to prevent them detecting your base, and to delay the next UFO in the wave.
The other effect that UFO shoot-downs have is to prevent the aliens gaining points from UFOs landing, although is only applies to Infiltration, Harvest, Terror and Abductions missions, if I'm reading the code correctly on Github.
And I am 100% rock-solid sure that the alien missions are not cancelled, ever.
And this can be confirmed if you check on Github the code that generates alien missions
The thing that is bothering me is that the UFOPaedia.org page has different values for the delay introduced on the original game, stating that they can vary between 1-9 days. Either I misinterpreted the OXC code or something else