Frankly I think you're both "wrong" as, unless there's more info I'm not aware of, we simply don't have enough real data to know what the true average time is for a given pool. Saying if all but one pool stopped that the blocks would continue on being generated every 10 minutes with the exact same difficulty is clearly wrong. As is saying that the "win" average is an accurate representation of a pools true average if they were the only one solving blocks at a given difficulty.
You should understand what "mining" is: it is finding a hash of a given block that satisfies a "rareness" condition: the difficulty. If the difficulty is, say, 1000, that means that only one hash out of a thousand satisfy this requirement. Now, the specificity of a cryptographic hash is that you cannot have the slightest idea of what it is, before you've calculated it. This means that each time you calculate a hash of something, you have one chance out of 1000 to have a hash that satisfies the condition. But it is really random. It could be the very first hash you calculate, and it could be only after you've calculated 2000 of them. However, ON AVERAGE, you will win one good hash every 1000 hashes you calculate, because, exactly, one hash out of 1000 is a good one.
Now, your hardware can calculate a certain number of hashes per second: it is your "hashrate". If you can calculate, say, 20 hashes per second, then you will need 50 seconds to do 1000 hashes. So ON AVERAGE, you will win a good hash every 50 seconds. But it can be after 1 second, or it can be after 200 seconds, because the lottery is random. However, ON AVERAGE you win a block every 50 seconds.
Now, bitcoin (and many other PoW crypto) have a self-regulating difficulty, so that the difficulty INCREASES until the average time of winning a block is 10 minutes for the whole network. However, this update of difficulty happens only once every 2000 blocks (2 weeks if we have, exactly, 10 minute blocks). In our discussion here, we are considering short time spans, with constant difficulty.
It means that the hashrate of the whole network is such that on average, the whole network wins a good hash every 10 minutes. If you have only, say, 10% of that hash rate, you will only win a block, on average, every 100 minutes. As the "winning of a block" is entirely random, the "moments of winning" by a given pool are rarely coincident. So MOST OF THE TIME, you win the block of which you find a good hash, because exactly at that moment, no-one else is winning a block.
It is only in those rare circumstances that you won a block and someone else did too, on the same old block, that one of them has to orphan, as decided by the other miners.