It is a commonly admitted fact that you should calculate the true wind with the apparent wind speed and angle (a vector), to which you add the vector of the boat speed and heading.
The trick is that the boat speed and heading should not be the one taken on the water, but on the ground. That means that you need COG & SOG coming from the GPS, and not the Boat SPeed and HeaDinG returned by the instruments (like speedometer and compass).
You are sailing is absolutely NO wind at all, and you have a current of 3 knots, taking you to the 270° true. The apparent wind you feel comes from the 270° true, at 3 knots. We assume that your boat speed - returned by the speedometer - is 0 knots, and we just don't care about the heading.
If you combine this apparent wind vector with the data returned by the GPS (COG=270°, SOG=3), than you appropriately find that the TWS is zero, as it actually is.
But if you use the Boat Speed returned by the speedometer, then you find a TWS of 3 knots, which is absolutely wrong!
I believe most of the stations computing the True Wind for you are in fact using the data coming from the instruments (and not the GPS). I need to check that..., but is that is the case, then there is a problem.