Each additional confirmation only means that the node that tells you about the confirmations has received and validated an additional block which has been added to its copy of the blockchain. That could be the exact same miner, and the exact same node. Additional confirmation does NOT "means that the transaction and the block containing the transaction have been validated by other miners and full nodes."
It was not nonsense. I was stating the general case because I didn't want to get into the weeds just to point out that 1 confirmation means something different than 2+ confirmations.
Yes, it was nonsense.
It was not a "general case". There is nothing about confirmations that has anything to do with whether or not any other nodes or miners have validated the transaction or the first block.
First confirmation means that a miner has included the transaction in a block (hopefully the miner, or pool, was smart enough to validate the transaction first, but they are not required to), and that your node (or a node that you are connected to) claims to have verified that the block from the miner is valid.
All additional confirmations only mean that more blocks have been added to the blockchain by the node that is reporting the confirmations to you. It is not an indication that anyone else has done any additional validation of the transaction or the first block.
That is the "general case".
The special case is that you *might* have heard about some of the additional blocks from different nodes and/or different miners. If that happened, then it is likely that those other nodes *probably* verified the earlier block before adding new blocks on top of it (although there have been instances of nodes and miners failing to do so in the past).