Am I the victim of Furnace fraud?

I used to live in an upscale condo, and after buying a house started renting it out. My tenant calls me and tell me the furnace is on the fritz. I go over and take a look. I lived there for 8 years and never had a problem with it. The furnace is a Carrier 58PAV07 that was installed in 10-1998. The issue was it would start up the burner for a few moments and then go out. It would cycle like this for a while before it would quit.

Not sure what to do and not wanting to leave my tenant without heat I called the HVAC company that installed the furnace in the first place. I expected to get a voice mail and would need to call them during work hours the next day, but nope they answered and said they would have a tech over in about an hour.

I needed to leave but my tenant was there. An hour later I get a call from the tech and he says "Oh it is a flame sensor. Easy fix, will cost 280". Ripoff I know but whatever $280 probably won't have an issue with the furnace for years to come. Then a few minutes later I get another call. "Your heat exchanger is cracked".

What!? He said "You need to come look at this, right way". After lots of insisting that I'll need to get a second opinion on it he convinces me to go over there. He shows me how one of the burners goes a different color and gets much larger than the rest once the blower starts. He says my heat exchanger is shot, I need a new furnace and it is unsafe. He turns off the gas to my furnace and sends a sales guy over. After some back and forth we settle on $1700 for a new furnace. (A number I was not very happy with I know HVAC markups are obscene). I set it up to be installed on the next day on the condition that the furnace isn't any longer under warranty. The salesperson says "Our company installed this furnace and while we don't sell Carrier anymore there is no way this unit has warranty and Carrier warranties don't transfer between owners anyways."

So the next morning I call Carrier and I give them the serial number for the unit. They inform me that the heat exchanger is under warranty. I halt the furnace install. Carrier is very insistent to me that I must use a contractor on their list on their website. Which is my area is a list of exactly ten. I call them all and only two return my call. Of the two one quoted me on the phone $1050 in labor to replace the heat exchanger. The other says they should look at it and confirm the heat exchanger. This contractor does a CO test and says that their detectable CO being emitted from the furnace, 8 ppm with a starting reading of zero. According to them, bad enough to warrant fixing, but not necessarily deadly. They quote me the same $1050 in labor to do the heat exchanger, or $1200 for a new furnace. Mean while I speak to the original HVAC contractor and they offer to replace the heat exchanger for $800 even. I say I'm leaning towards just replacing the heat exchanger, and the second contractor gets back to me and says they can't get the part for three weeks. So I say fine lets just do the whole furnace for $1200.

So today I go over to my condo and the furnace is sitting in the hall while they are about 75% though installing the new one. I use this an opportunity to inspect the heat exchanger myself, and I can't find a crack or defect in it anywhere. Except for one issue. A sheet metal screw near the burner that was burning abnormally is missing, leaving a whole though the heat exchanger. How did that happen?

So is it likely that the first HVAC tech could have removed the screw in an attempt to get me to buy a new furnace and is it possible the second HVAC company didn't notice or didn't want to tell me?

TL;DR; Two HVAC companies looked at my furnace. Both agreed that the heat exchanger is bad. The second was way less expensive than the first. I inspected old furnace and only found a missing screw in the heat exchanger.