Some (large) EU governments are making the case for digital companies to pay "their fair share of tax". The key underlying assumption is that companies in the digital space are not doing so right now. Governments also assume that there is a substantial source of untaxed profits that is waiting for the embrace of the taxman. The European Commission is now considering "revenue taxes" on those companies that under some definition can be called "digital corporations". In this paper, we provide a critical assessment of the underlying reasoning of the European Commission and those EU governments that currently are in favour of targeted taxes on digital revenues. There is indeed a good case to make for fair taxation and that uneven effective tax rates can distort competition and lead to smaller tax revenues. However, those that are calling for higher taxes on one particular group of firms - digital corporations - have yet to present the evidence for why that is motivated by principles of fair taxation. The European Commission's "hypothetical" estimates for effective corporate tax rates (ECTRs) do not reflect the high effective corporate tax rates of most corporations that operate in the EU and outside EU Member States, including the world's largest digital enterprises. In addition, the European Commission's selective focus on digital companies that are big on "stock markets" mixes up market capitalization with corporate income. Thereby, the focus on the world's "top 100 companies by market capitalisation" and the world's "top 5 e-commerce companies" hardly reflects the reality of the digital economy and profit levels among different, often highly diverse, firms. Real world financial data show that the average corporate tax rates of many digital companies actually exceed the European Commission's "hypothetical" estimates by about 20 to 50 percentage points. Ideas to slap a targeted tax on digital revenues clash with the EU's top policy priorities for the digital economy. It is therefore remarkable that such taxes even are considered. A tax on digital revenues would not only stand in opposition to tax efficiency and neutrality; it would also undermine digitalisation, European integration, and the Digital Single Market.