As someone who used to work on and build industrial battery chargers, yes, charging the battery right before starting the engine could be hiding a worn out battery. But I doubt that the tender (or tender/charger type) is your issue.
If for example your charging system on the bike is not in good shape, or you have some parasitic current draw through either a minor short or aftermarket accessories, that too would allow you to start the engine fine when you've fully charged the battery at home, and the battery may last long enough or get enough charge to keep the voltage high enough to run the bike while riding, but then give you starting issues on your return journey home.
Battery tenders are designed to do just that, tend to a battery that is in good condition and will just be sitting for a while. While it may be sort of nursing your battery along, I would be inclined to say your issue is upstream of the battery tender itself, or what type of tender/charger it is. Almost certainly the battery or charging system health is your issue instead, especially given the age of the battery you mentioned. Well worth replacing regardless, and cleaning the terminals on the harness too.
None of my bikes over the years have needed to be on the battery tender in order to start, even when sitting for a whole winter in my garage. I still use a battery tender on my seasonal bikes, but the tender always reports that the battery is still full or very nearly full every time I plug it in. Never had starting issues in years prior to me owning a tender either. I also usually replace batteries in my bikes well before any noticeable issues arise, usually every few years, or if the battery has been discharged too much due to some issue before. That can damage the plates in the battery and accelerate wear.
-Mike