First rule, check for voltage drop/high resistance in both the positive and ground circuits. The best battery in the world can't overcome high resistance, especially when cold.
Second rule, do a proper load test (which is what that dealer should have done) if you want to determine the real status of the battery. If it passes a properly performed load test with flying colors, it's not a battery problem.
Three years is nothing for a properly maintained AGM battery. I've had my OEM batteries last 6 and 5 years on the last two bikes, both standard Harley AGM batteries. The ones on my 4 wheeled vehicles have lasted at least 5 years as well. Rather than throw away batteries based on age, I recommend a greener approach of changing them out (and recycling them of course) when proper testing indicates they need to be replaced.
Jerry