I am not an arbiter, but I find existing answers lacking in detail.
This particular rule became stricter on July 1, 2017. Until then, the relevant rules read:
Provided that he first expresses his intention (for example by saying “j’adoube” or “I adjust”), only the player having the move may adjust one or more pieces on their squares.
Except as provided in Article 4.2, if the player having the move touches on the chessboard, with the intention of moving or capturing: [...]
In those times, player's intention was theoretically the sole basis of making the arbiter's decision about a touch-move claim. The rule even guaranteed the right to adjusting the pieces, conditioned on expressing the intention to adjust the pieces somehow prior to touching them. That didn't mean that a player's claim about their intention would have been automatically accepted by the arbiter; the player would have to explain how they expressed their intention, and even if they actually said "j'adoube", there could have been a dispute over whether this was said first, i.e., before actually touching the piece or right after.
In case of a piece lying on the floor, under those rules, the intention to adjust would be considered unambiguously expressed by diving under the table and picking the piece up there; note also that the rule doesn't extend to pieces lying off the chessboard.
Arbiters tended to enforce touch-move, but some players got away with high profile situations widely believed to be violations of touch-move because it is difficult to rule about "intention" with certainty.
On July 1, 2017, the following stricter wording was adopted.
Only the player having the move may adjust one or more pieces on their squares, provided that he first expresses his intention (for example by saying “j’adoube” or “I adjust”).
Any other physical contact with a piece, except for clearly accidental contact, shall be considered to be intent."
Except as provided in Article 4.2, if the player having the move touches on the chessboard, with the intention of moving or capturing:
one or more of his own pieces, he must move the first piece touched that can be moved
It may appear to us laymen that little changed. However, this update of rules was commonly understood by arbiters at that time as a directive to decide any gray cases toward assuming intention to move on the part of the player who has touched a movable piece on the chessboard. If the prior rules generated some false negatives (getting away with very fast violations of touch-move), then the new rules might be expected to generate some false positives (punishing someone for failing to say the equivalent of "j'adoube" in a situation where they should ideally have been trained to say it automatically). I believe that extremely strict enforcement is more likely to happen in top tournaments and less likely in fun events or young players' tournaments, but in the end it is still up to the arbiter who doesn't always have a video recording of the situation available.
From my perspective, this particular question most likely does not concern a case of touching a piece on the chessboard. Most likely, the piece was just held while it was being repositioned; it might also have been dropped from a height to the chessboard, or dropped and then touched again, or held, let loose and then touched again. So the touch-move rule might or might have be available for consideration, and the arbiter may not have seen the exact minute movements of the hand which could have made the dispute just another gray area case in their mind, so perhaps they automatically went with assuming the intention to move as dictated by rule 4.2.2.
BTW, it would be a mistake to claim "clearly accidental contact" if challenged like this. That phrase is never referring to any accidental contact between pieces and spectators; "clearly accidental contact" refers to cases like the player toppling down one piece by their elbow while clearly reaching for another one with their hand. Claims of "intention to adjust" and "clearly accidental contact" are logically incompatible with each other.
An active player playing by the new rules should ideally say "j'adoube" or the equivalent between picking up the piece from the floor and repositioning it onto the chessboard. This should become an automatic instinct these days, a more important one (rating wise) than being able to mate with a bishop and a knight under time pressure. Another important instinct is staying calm and factual and trying to claim one's own transparency of intention in case of any dispute about the intention. Of course, it would be poor sportsmanship on the part of the opponent to claim lack of expression of intention to adjust if there was no doubt whatsoever about the intention to adjust itself; and an arbiter still has some freedom about what to consider "expression of intention to adjust" in a given situation. They will normally have to rely on claims and counterclaims as to the facts of the case as made by the players themselves.