Did Northern think that a Saturday with good weather would not attract prospective rail travellers to Windermere and that a 2-car unit would suffice?
Had Northern got any 3 Car formations available ?
If people are fully aware that a two-car unit is unlikely to satisfy demand, then to say "sorry, folks, we didn't have a three-car unit available" is on a par with failing to run a service altogether and saying "sorry, folks, we didn't have a train!". For a TOC to find themselves suddenly, and unnecessarily, overwhelmed with passengers I find quite unprofessional.
Of course, there is a problem with Oxenholme-Windermere in that a three-car unit is the largest train which can be accommodated (I presume) and also, only one train can be on the line at any one time. However, Northern, like most TOCs, have a reduced requirement for rolling stock on a Saturday, so finding a three-car unit to use shouldn't have presented a problem. If it had done, they could have always resorted to partial coach substitution, e.g. run a coach non-stop from Oxenholme to Windermere, it would do the journey in a time comparable with that of the train, traffic permitting. Whether it would have been in Northern's interest to do that is another matter.