The spiders and probably other critters poolman is referring to wind up in the burners and gas manifold. By the time the gas hits the burners it is at a really low pressure so it doesn't take much to mess up or block the gas flow. Never took them out of a pool heater but I suspect the burners themselves should be easy to remove. Once you get them out you'll see how they are vulnerable to obstructions. Once they do light if you can look inside you may be able to see if the flames are steady, even, and blue with orange tips. I think you want the flame tips to be slightly orange or yellow. Too much air and the flame is blue, too little and it turns yellow or orange indicating incomplete combustion. The owners manual should tell you how to adjust the air vents to get the right gas/air mixture.
Al