Did you play Link to the Past or Link's Adventure?

Yes. Although LttP required more items to beat specific dungeons, you could still do a bit out of order. As the series has progressed, each title brought more and more linearity to the game.

So you think that Zelda is diverse because it's linear? Give me a break. What it's called is bad game design. When they (the developers) are forcing you to get specific items or requirements to pass a certain point, they are taking out the 'adventure' aspects of a title. Regardless in Ocarina of Time (or any other modern Zelda), you have to get specific items to complete levels, no matter what you do.

Although Fallout 3 has (at times) generic level design, and few puzzles, the fact is that the adventuring aspects far surpass that of Zelda, which is what the OP is arguing - Zelda has lost its true 'adventuring' roots, and delved more into an Action/Puzzle game with set backdrops, claiming to be an 'adventure' game when you aren't adventuring - it's all pre-set.

The argument is that (from my viewpoint) that Zelda needs to have more of the Fallout 3 mentality of 'yes, you can venture to Gerudo's Fortress without the hookshot, but the enemies are going to be overpowered, and kick your butt. If you do manage to beat that fortress, you'll have access to end-game powers that'll make the rest of the game a sinch' and less 'stop! You must complete every dungeon in order! This is not an adventure! You can't go there for another 10 hour' tease.

You CAN have non-linearity in an adventure game, and still have it be great - look at Zelda 1 & 2. Both were non-linear and allowed you to complete dungeons in a semi-linear fashion. Of course, the later Zeldas have abandoned that formula, which is why some are taking up arms with it.

Puzzles could still be engineered to be tough - but have answers that don't require you to have a very specific item (such as a hookshot, boomerang, or such). Zelda would then reward you for both linear (easy to beat) and non-linear (uber-items early in game) dungeons.

One of my most treasured memories from early games was that some RPGs, such as Dragon Warrior 3 (DQ3 for the rest of you) had areas that you could access early on that contained very high-level monsters. If you managed to somehow beat the battle, you would gain 2-3 levels per battle, and sometimes gain weapons that, under normal play, would be unavailable until hours later. Heck, Chrono Trigger gave you that in Medina Village in 1000AD with the 65,000G items - If you were smart (like I was), you could save up enough money to buy a sword for Chrono immediately upon entering the village, and have a sword so overpowered, you could use it for the next 10 hours until you could re-purchase the said weapon in 12,000BC (which was quite a bit further into the game).

Do you see at what I'm getting at? Games need to reward players that draw outside the lines, and do things the hard way, by giving them access to end-game items if you can manage it. Fallout 2 did a good job of this as well - If you learned the right moves, you could access Power Armor within 20 minutes of starting the game (which, under normal circumstances, would take you hours to get).