I'm immensely sceptical of whether Labour will actually do exactly what they say. But asserting they will do the exact opposite of what they say as if it were some undeniable truth is just as silly and extreme. The truth as you suggest is probably somewhere in between.
I expect like many that if Labour are going to do some fund-raising it would be through some wealth taxation like capital gains and not income related. I think they will be pinned down to that manifesto pledge of not raising income or VAT taxes because, quite simply, if they didn't, it would be political suicide. Who knows though, it seems like our political class enjoy a bit of that.
As long as the tax bands remain broken and frozen, the tax raising is happening anyway in absolute terms, even if the tax policy isn't changing.