The problem is that guaranteeing a minimum means that a low-paying job that potentially pays a little more may result in no increase in total income : The pay being offset exactly by a withdrawal of the government handout. This is equivalent to a huge implicit tax rate for poor people, and is common effect in developed countries with so-called safety nets.

By giving the basic income to everyone equally, everyone has an incentive to earn more money at every point on the wage spectrum. Higher earners will still pay higher marginal rates (likely everywhere else). But the situation of the highest marginal rates being experienced by the poor (which is common) is eliminated, as are the expenses of administering complex benefits and means-testing regimes.

It doesn't seem to be available in English, but the organisation that wrote the initiative say so on their website[1]. They say "It is added to other revenues". So yeah, the intention is really to have an unconditional basic income for everybody and not some sort of negative income tax scheme as has been proposed elsewhere.

[1] http://bien.ch/fr/page/initiative-federale#revenudebase

You are talking about Guaranteed Minimum Income, which is very much different from a Basic Income (more descriptively known as an Unconditional Basic Income, emphasis on "Unconditional").

The article says "a basic income for all adults", not a basic income for all adults below a certain income threshold.