This could already be a serious problem, or soon become one. Carbon Monoxide (CO) is very dangereous. IN fact, it's a killer! If the flu is deteriorating, then it's deteriorating as you've already seen. The GOOD news is you can see the 'facts' that the Contractor is saying.
In the least, get 2 more estimates for repair. See what they say and DO talk to them about what the 1st guy said. And also, boilers these days have certain requirements by both Building Codes and Use. They're meant for your protection and for the efficient operation of the unit. If he says the unit requires A and B and so on, I can't imagine him blowing steam (not to coin a pun.) Get more estimates and ask more questions.