However, I've had a professor or two
that harped on the use of strict,
formal UML, as close to the spec as
Ask your professor when was the last time he used that approach on a real system. Seriously.
I try to be as formal as possible when it comes to UML, but only if/when it makes sense. Zealots on both side of the spectrum (from cowboys to uptight formalists) fail to understand that.
There are contexts in which a less rigid approach (like the one you personally use) is the best approach to follow. A good example is for small systems or changes, where requirements are small and not fully defined; the group in charge is efficient and effective; it is more important to get it out than to get it perfect. It is done iteratively and some deficiencies are acceptable.
Or maybe you are in a stage where you are doing guestimation and sketching as opposed to a full formal modeling phase. Those are examples that would come to mind.
At other times, you need a rigid formal UML approach. For example, you might be contractually bound; you have a very large number of developers in multiple teams (possibly distributed); the scope of the project might be in years; it is a very large system (including software and hardware components); the cost of failure is high, etc.
At other times, you have to use something else instead/in addition to UML (actual mathematical formal models like petri nets, CSP or temporal logic.) Example of this are real-time systems, systems where failures are catastrophic (medical devices) or where you are contractually bound (.ie. as in Europe when developing transportation systems.)
It all depends on the circumstances and what we expect to gain from each approach. A professor that harks on sticking to formality is simply being a blind zealot. The world of engineering is not a black-n-white, right/wrong dichotomy. It is a world of intelligent trade-offs.
If you are intelligent enough to use a casual, informal model in a manner that is effective and appropriate to get the job done, then so be it. By the same token, you will be expected to recognize when NOT to use an informal approach and/or when NOT to use a formal one.
Having said that, you have to play it by ears with professors. Give them a bone so that they give you a grade, and if that means to finally bow to their zealot mantra, that's fine. You know what works for you, and hopefully, you will know when to use what and how in the real world.