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Let's analyze this. Hero: Sinister. Difficulty: Hero. Map: let's say, the Dragon Pass. Start: 9 Scouts, 3 Beasts, city level, and hero level 1. Day 1: build Scouts and gather ore – guard duty with 4 squads of 22 peasants each. With Magic Arrow, you can do this without losses. Day 2: build Scouts and return to the city, then get Griffins. You'll have 16 Scouts. Take the lumber mill; guard duty with 2 squads of 15 Dryads each. Mana hasn't fully recovered yet, and there's no well, so you'll lose 2-3 Scouts or lose a day in the city. Day 3: build the Town Hall and move towards the Sulfur Mine, or move to the city for Beasts – but there's no point in that. Day 5: build Furies and attack the Sulfur Mine. Guard duty with 4 squads of 16 Spearman. With 16 Scouts, you're dead.
In the first week, it's unrealistic to capture all the mines you listed, and not just because the guards are strong, but also because you simply won't have time to reach them. Or are they all located right next to the castle, so you can take three mines in one turn? But in that case, we're playing different games.
So, who's the one making outlandish claims here?
Regarding Witches, I agree, but I was describing the best-case scenario. As for Utopians, you can try capturing them towards the end of the second week, or at the beginning of the third.