I don't see how anything could be damaged by starting the generator while on shore power. If you have any significant loads active, you will be stressing the transfer switch and the generator, and so that would not be recommended, but it shouldn't in itself cause damage to anything. (For that matter, starting the generator or connecting to the line under load is not recommended regardless of the circumstances.)
The transfer switch is designed to be a break before make switch—that is, the shore power is disconnected before the generator is connected, and vice-versa. Directly connecting them together is impossible by the switches mechanical design. If the generator were directly tied to shore power, that would be very bad and would probably destroy the generator (and maybe other systems in the area). Bear in mind that the generator head is basically a large electric motor of five or more horsepower. Connecting it to the line voltage if it's not well synchronized first will cause a very sudden and very strong torque, and stuff will break. (What stuff? My guess would be the crankshaft or connecting rod of the generator engine, rather quickly followed by the generator electronics, but it's not something I care to experiment with to find out for sure.)
If starting the generator while on shore power were truly a big problem, surely the manufacturer would install an interlock in the starter circuit (which would be quite straightforward to do) rather than merely putting a line in the owner's manual that frankly many people won't bother to read.