If the tub is probably under warranty I would not give up because paper work is not available. The unit will have a stamp on it as to who the manufacturer is and then someone will know who the developer is and who installed it. There are other methods of proving how old the tub is other than with documents. Indeed, I am surprised that the association and/or the developer is not assisting you in this manner.
Yes, there are many cases that discuss who is responsible for what in condo cases. Indeed, years ago when I was practicing closer to this area, I worked on a few including a case that asked who is responsible for condensation inside dual pane windows. The issue is whether something is a common element or not. Often in law we have to look for analogies to find the answer. Your dishwasher as an example. If it leaked, warranties aside, you probably would have no claim against the corporation any more than you would if it was a broken fire place or light fixture.
Having said that, there could be something hiding in your bylaws or in either insurance policy that could bring you the answer. That is why I stated that this is primarily contract law. What is covered and is not is written and that is more certain than the opinion of any agent. Of course, I cannot read any of those materials.
So, a close look at the bylaws and the policies is where this investigation has to start. I am concerned however that the Alberta CONDOMINIUM PROPERTY ACT states "a corporation is not required to place and maintain insurance against perils to which the common property is not subject." That does not mean that they are not covered however. They just state that they are not.
Searching for cases on any legal issue is a bit of an art but you can give it a try at the following link. I spent about 30 minutes but found no joy for you but such research takes a lot of time. The site is not user friendly but it is free and very useful when you get the hang of it. I searched for cases in all provinces and not just Alberta. You want to find a foot in the door and then work backwards. On the first search line you would enter condominium and then "and" followed by different search parameters using the analogy approach. They are in quotation marks like "leaking bathtub". You will get cases using that but none that are definitive.
Nothing I saw in my research indicated to me that a bathtub is anything other than the property of the owner.
There are other resources to find law that could support a claim. The law courts and law schools in Calgary and Edmonton have libraries with helpful librarians. These libraries are open to the public and have sections on Condo law. Look for text books and not cases first. You should find texts specific to Alberta but any text will do to start. In each you will find the debate on what is inside or outside a Unit and you will see that what is inside is generally the responsibility of the owner.
Your next resource is a live lawyer who can look at documents. Below is a link to the lawyer referral program. Call them and ask for lawyers who practice condo law. You will be given a few names of lawyers who have agreed to meet with clients initially at no charge for up to 30 minutes. I worked more than that looking so you may find a fee is requested especially if you want them to read the small print.
However, expect the first reaction to be that the tub is your responsibility. On the other hand, a person who practices in this area every day might have an angle for you off the top of his/her head.
This is just a blog and not law nor a legal opinion even but I found this directly on point while trying to assist.
So, it is not possible to see if any insurance policy applies without reading the policies. If a warranty still applies, it should be investigated even if there is no paperwork. Your have other information resources but your challenge is the position that the tub is not common property.
I certainly gave it a go despite my instant reaction on the facts that this was about bylaws and contracts.
Please consider accepting my answer for my time. I am interested and would schedule a follow up in a month or so. If you need any clarification of my points, please reply.
My best to you,