I don't know who told you they won't put out that wattage, but they're wrong.

As you know Generators have two wattage ratings. Running (In this case 15,000 and 17,500 watts) watts which is the constant output. Then you have Surge (Something like 22,500 in both, I think) which the engine can briefly put out to "jump start" high voltage appliances like Air Conditioners.

People assume that a 62.5 amp (15,000 watt) generator with a 50 amp rated plug can only put out 50 amps through that plug. In reality it can put out as much as it wants. Most plugs that're 30 or 50 amp on generators have their own breakers on it and the breakers are usually rated at at least 80 amp so the plug can pass on the surge wattage to the appliances wired to the generator.

They just call them 20 amp, 30 amp and 50 amp plugs because that's what traditionally that plug size runs and/or has been officially rated to run years ago.