The modern mixed economy that every Western nation has is called that because it is a mixture of capitalism and socialism.
Its true that BI is consistent with that mix, but that's not a counterargument to it being from the socialist side of the capitalist/socialist divide. (Of course, the utility of that divide and the breakdown of arguments over economic arrangements into "which side of the divide does that fall into?" followed by "if capitalist, good; if socialist, bad", or vice-versa, is dubious.)
Its true that BI is consistent with that mix, but that's not a counterargument to it being from the socialist side of the capitalist/socialist divide. (Of course, the utility of that divide and the breakdown of arguments over economic arrangements into "which side of the divide does that fall into?" followed by "if capitalist, good; if socialist, bad", or vice-versa, is dubious.)