Some people ask whether welfare benefits should be universal of means tested. (By universal we mean that everyone gets the same amount, no matter what their circumstances, and by means tested we mean that people's other income and circumstances are taken into account when calculating how much they receive.)
To answer this question, imagine two countries, Universalia and Meanstestia.
In Universalia, they have a universal benefit: everyone gets £100 a week. On all their other income, they pay tax on it at 30%. Alice, a citizen of Universalia, earns £220: she pays £66 in tax and ends up with 100+(220-66) = £254.
In Meanstestia they do things differently, in that they have a means test. If you have no income, you get £100 a week, but for every £1 of income, that is reduced by 30p. Then when you get no benefits you start paying income tax on all your income, at 30%. Bob in Meanstestia also earn £220. His £100 benefit is reduced by £66 so he gets (100-66)+220 = £254.
It's easy to see that whatever the level of your initial income, you get exactly the same amount under both systems. So in that respect they are the same. And if two systems always have the same outcome, then they are in one sense the same system, and there's no principled reason to prefer one over the other. (There may, of course, be administrative reasons to do so; or political reasons, in that one system is easier to sell to the voters than the other.)
So asking "should the benefits system be universal or means tested?" is the wrong question. As is "should a particular benefit be universal or means tested?"
Instead, one should ask, if a person is in receipt of a benefit, and their other income goes up by £1, how much should they end up better off?
Usually when I have heard people talking about means tested versus universal benefits, they have been talking about benefits you only get in specific circumstances: for example "should child benefit be means-tested or universal?" I think your logic doesn't apply to such cases. I think if you wanted to make a universal and means-tested version of child benefit be equivalent, you would need to fund the child benefit on taxes that are only levied on people with children. The reason your example works is because you've assumed that the potential benefit recipients and potential taxpayers are the same people.