Honestly, there's an extent to which they're both correct. The initial expedition that would become the Gallipoli campaign did intend to use obsolete pre-dreadnoughts to force their way through the straits, threaten to bombard Constantinople and knock the Ottomans out of the war. (Before you say that sounds preposterous, please remember that the Ottoman entry into the war was occasioned by one German battlecruiser (SMS Goeben) and a light cruiser (SMS Breslau), which forced their way into the Black Sea, were "bought" by the Turks, and conducted naval operations against Russia while still under German command.) I'm going to pause here and refer to an older answer of mine:

The Straits were known to be mined, and also to be defended by heavy guns. In the brutal logic of the war, Churchill figured that even losing several older battleships, with their crews, was less bloody in the long term than infantry attacks on the Western front. The problem with the naval expedition was that the Ottomans had a surprisingly stout interlocking defense, both of lines of mines and also of large guns. There's also a pretty significant current in the Strait. So an initial effort by battleships to force their way through was marked by an early defeat (and a bit of timidity on the British part when they discovered the mines).

The minesweepers (converted fishing trawlers) the British then bought to the Straits were deeper in draft than the anchored mines, which tended to depress morale among the crews of the sweepers. Nevertheless, they successfully swept at least two of the lines of mines before fire from shore batteries knocked out several of the minesweepers. At that point, they rethought their approach and brought in HMS Queen Elizabeth to try to knock out the shore batteries by firing over the peninsula (from the Aegean side). This was actually fairly successful, and the Turkish batteries were running low on shot and becoming desperate before the battle of March 18, in which an undetected minefield sank three of the Franco-British battleships and forced a withdrawal. (It's arguable that had the fleets pressed on, the Ottomans might have withdrawn from the peninsula; we will never know. Ottoman morale was wavering and the batteries were nearly silenced; the fleet's withdrawal allowed them to restock and replenish.)

In any case, the failure of the ships themselves to be able to knock out the guns led to a call for a landing at the Dardanelles, using troops to secure the batteries. At that point the Strait could be swept of mines at the fleet's leisure.

So that's the standard narrative that's addressed in your question marked 1 above (the first one marked 1, anyhow, stupid Reddit formatting :-) ).

Where the campaign really started to go awry was after that happened. I would take a bit of issue with

old-school admirals overly attached to them for emotional reasons insisted on mounting a land campaign to save them, the exact thing the battleships were deployed to try and avoid, and the tail ended up wagging the dog.

it's not just that the old-school admirals were attached to the battleships, each one carried 1,500 or 2,000 sailors as well, even if they were "only" reservists. I am not as well acquainted with the land operations. But the basic issue as I understand it is what you identify as delay -- namely, that it took a number of months after the initial naval withdrawal for the land operations to commence, allowing the Turks to dig in and heavily fortify the peninsula. It's certainly debatable whether a coup de main with landing parties would have been able to carry the batteries before the withdrawal, as Turkish morale was running low, but that's now in the field of alternate history where we do not go.

If you're interested in the debate over the land side of the battle, you could do much worse than read this excellent AMA from u/margaretharris.