Figure 2B of the installation instructions you provided reads “ Secure with 1/4 inch sheet metal screws“.
It doesn’t say recommend. For this particular manufacture it is a requirement as it is in their installation instructions. Sounds like you boys have some Bill Bob HVAC contractors up there.
Please refer to the instructions, this is what their installation instructions say (once again, the diagram is for illustration if and when screws are used):
Using sheet metal screws when you have multiple connectors and fittings that can act as a swing joint is just a good practice. I would never trust the lock joints to keep everything secured.
Everyone can recommend whatever they want this is always my recommendation. Proper supports with sheet metal screws go along way.
At a certain age, that would have been terrifying to see…
The only thing you should concern yourself with is the unsupported flue.
There are a lot of things you must consider and that is not your job. Length is only one factor that must be considered. Induced draft fans are required (not recommended) if the flue does not meet draft design.
Size of furnace.
Diameter of flue.
Length vertical.
Length horizontal.
Number of fittings.
Does the furnace have induced draft.
Flue temperature (condensation from too much draft).
Anyone think that supply duct is balanced for this “Custom Job”?
I think all the conditioned air is going out of those last three ducts at the end.
Thanks to everyone for replying. Y’all always give me more information than I ask for, but that’s great!
That’s because you will never ask a question about something that you don’t know even exists or is an issue or concern… or not! 
I agree Jeff, but how many times you ask licensed contractors like an electrician on a form a question and you get a hundred in-depth answers about 50 of them say you’re stupid and some type of way and yet almost every comment or explanation contradicts each other. It’s like every contractor thinks the way they do it is right and everybody else is doing it wrong. Id believe it, except everyone’s always so sure of themself.
I do not know if this helps but 503.10.9 Length of vent connector.
The maximum horizontal length of a single-wall connector shall be 75% percent of the height of the chimney or vent except for engineered systems. The maximum horizontal length of a Type B double-wall connector shall be 100% percent of the height of the chimney or vent except for engineered systems.
But a single wall vent is not type-B vent as is the title of this thread. 
Read further, Larry.
Type B double-wall connector shall be 100% percent of the height of the chimney or vent except for engineered systems.
