I disagree with both. Letting people know who you're against is a powerful weapon, and helps people trust you. For example, its not uncommon to, as England, tell people you're going after France. In doing so, you build up people's trust, and so may find it easier to get assistance.
Basically though, any time someone tries to generalize diplomacy I find the answer is no - there are so many possible ways to play it all comes down to your style

I like telling people that I will move to Spain+Portugal+Belguim as France and I keep my word which gains trust

You're successful with a three build France? I'm pretty sucky at France regardless, but in games I tried to actually posses Belgium, instead of decide who else gets it, I crumble. Three builds? What're Germany and England supposed to think? Three armies Germany panics, any fleets and England does. Even a Mediterranean fleet scares Italy.

Maybe I'm just doing it wrong.

"For example, its not uncommon to, as England, tell people you're going after France."
But do you tell that to France?

"Many Italy's are still on everyones side after 1901."
I didn't consider Italy too closely when I thought about this; I'll post power-by-power reasoning soon.

I agree with the first half but not the second. I'd say that in the second half of Fall 1901, ideally everyone still thinks you're on their side, but more likely than not your target will have figured it out. If someone other than your target gets the idea that you're against them, hoo boy, now you're in trouble.

I'll do a quick run-down for my minimal reasoning of the Fall parts.
(Disclaimer: I'm a newb, at least relatively speaking. I have some experience, but not enough to be especially reliable for knowing this)

England: France, Germany, or both will probably be against you, depending on the outcome of Belgium.
France: Again, it's mostly about Belgium - either one of E and G supported you in or you supported one of them in, and you're probably allying with that one against the odd man out. Again, this is minimal reasoning, so this won't even cover Channel bounces and Burgundy.
Germany: Even if you play it safe and go for only two builds, the other powers fighting for the Balkans will be displeased if you don't bounce Russia from Sweden if you're able. Also, Belgium.

Russia: If Germany bounces you from Sweden, you know he's not your ally; if Turkey moves on BLA, you know he's not your ally; if Austria tries for Galicia, he's either not your ally or a very distrusting ally. Also, once the Balkans explode you've probably either been attacked or helped by one of A and T, who will be your ally against the odd man out AGAIN, or you've caused an IR vs AT to happen.

Too tired to do Austria, Turkey, and Italy now. Sleepy.
OH HEY DISAMBIGUATION NOTE. Spring '01 and Fall '01 aren't really consistent about what phases I mean. Spring '01 = Before anyone's moved, Fall '01 = After two sets of moves. So Winter '01, I guess, would be more accurate.

Normally I try to keep as many allies as I can and keep everyone on my side in Spring '01. This backfired on me recently though - as England I had decided that I wanted to go for France and solicited Germany's help. He agreed and I thought we were going to be solid allies.

However, since I had tried to make alliances with basically everyone except France the rest of the players on the board got suspicious of me and France, Germany, and Russia all attacked me.

I'm still (barely) hanging in there... :(

Depends on what country you are. If it's say, Russia or Turkey, Turkey especially, then I guess I agree, but if you're good, or the others are stupid, you can keep them blind for quite a while.

how would not making alliances with France make people suspicious of you?

I would just take advantage of you while you attack France, with no home SC's and a downed france your much less of a threat

I totally agree with the original post. You have to be friendly with everyone in the beginning, but that can only last through Spring '01. For Fall '01, some other players will begin being suspicious of you after your first moves and the same will be true of you based on some other players' moves. After the first year, there should be no major secrets as to who is allied. However, those first alliances may only last a few years. The next round of stabbings soon occur and new alliances can even form. All of that is the beauty of Diplomacy.

Your original post should have specified that at the *end* of Fall 01 is when people know if you've screwed them or not ;)