Not taking into account the various reboots and changes in the timeline, there are two things that can explain why Graham didn't believed in aliens:
- First thing: a lot of the aliens encounters are erased from memory, either by the aliens themselves or some other force.
For example, you forget the Silence as soon as you look away from them. The Monks, the owners of the pyramids seen last season, erased themselves from memory.
From Lie of the Land:
(Sitting on the pedestal of a now-destroyed Monk statue, just the inner metal support sticking up.)
BILL: This is exciting, isn't it? You know, kind of, it's like a turning point.
(The Doctor is pouring a drink from a thermos.)
BILL: Humans have learned that they can overthrow dictators and stuff, they just have to band together.
DOCTOR: Well, it's not quite as simple as that. You, Appalling Hair.
(A passing student looks up from her 'smart' phone.)
DOCTOR: This thing that we're sitting on. What is it?
STUDENT: Er, we thought they were just like filming something here or something?
DOCTOR: Thank you. Very helpful. Now go away, or something. You see? The Monks have erased themselves. Humanity's doomed to never learn from its mistakes.
BILL: Well, I guess that's part of our charm.
DOCTOR: No, it's really quite annoying. Anyway, I mustn't keep you. Three thousand words. The Mechanics of Free Will. Now six months overdue.
- Second thing, and perhaps the most important, most of the humans do not care about any strange happenings, little or big, and wouldn't believe it anyway.
The Doctor says it clearly in Journey's End:
SYLVIA: But the whole world's talking about it. We travelled across space.
DOCTOR: It'll just be a story. One of those Donna Noble stories, where she missed it all again.
Donna noble, after having her memory erased in the same episode, wouldn't believe it when her friend on phone told her about the aliens that kidnapped Earth and the incredible sight of so many other planets in the sky.
DONNA: My phone's gone mad. Thirty two texts. Veena's gone barmy. She's saying planets in the sky. What have I missed now? Nice to meet you.
(Donna is on the phone.)
DONNA: How thick do you think I am? Planets. Tell you what that was, dumbo. That's those two for one lagers you gets down the offy because you fancy that little man in there with the goatee. Ha ha! Yes, you do. I've seen you.
DOCTOR: Donna? I was just going.
DONNA: Yeah, see you. I tell you what though, you're wasting your time with that one, because Susie Mair, she went on that dating site, and she saw him. No, no, no, no. Listen, listen, this is important. Susie Mair wouldn't lie. Not unless it was about calories. Ha ha ha!
Or, on a less dramatic scale of events, nobody notices or care that an out-of-date blue police box suddenly appears in one of the major places in Cardiff, right in front of the Welsh government building if I'm not mistaken, and stays there for some time before vanishing without a trace, all of this in broad daylight. As said in Boom Town:
MICKEY: Wait, the Tardis, we can't just leave it. Doesn't it get noticed?
JACK: Yeah, what's with the police box? Why does it look like that?
ROSE: It's a cloaking device.
DOCTOR: It's called a chameleon circuit. The Tardis is meant to disguise itself wherever it lands, like if this was Ancient Rome, it'd be a statue on a plinth or something. But I landed in the 1960s, it disguised itself as a police box, and the circuit got stuck.
MICKEY: So it copied a real thing? There actually was police boxes?
DOCTOR: Yeah, on street corners. Phone for help before they had radios and mobiles. If they arrested someone, they could shove them inside till help came, like a little prison cell.
JACK: Why don't you just fix the circuit?
DOCTOR: I like it, don't you?
ROSE: I love it.
MICKEY: But that's what I meant. There's no police boxes anymore, so doesn't it get noticed?
DOCTOR: Ricky, let me tell you something about the human race. You put a mysterious blue box slap bang in the middle of town, what do they do? Walk past it. Now, stop your nagging. Let's go and explore.