Actually, if you notice, the Appleman chart, which you say, can't be debunked, clearly states that contrails will form with extremely low humidity in extremely cold environements. The last line (the unbroken black one) shows that.
The two most important lines on the chart are the 0 percent relative humidity line and the 100 percent relative humidity line. If the atmosphere were colder than the temperature indicated by the 0% line, a contrail would form even if the relative humidity of the atmosphere were zero
Remember water vapour is also introduced to the environment from plane exhaust when it pases through a parcel of air.
Did you take into account vapour pressure, supersaturation and jet strream location?



