Confusion regarding Nyquist Sampling Theorem
It could be interesting to start from an history of this theorem in Interpolation and Sampling: E. T.  Whittaker, K. Ogura and Their Followers, by Butzer et al. 

Putting history aside, the main thing with the basic theorem is that one should refrain to say that the rate  "should" or "has to" be above something. This is could a sufficient, but not a necessary condition. One version is, with an "if": if $X(f)=0$ for $|f| &gt; B$,  sampling at a rate above $2B$ theoretically allows you to recover the signal from the  regularly sampled sequence:



There are milder versions, but this one shows that you ought to be especially careful if you choose, dangerously, $B$ such that $X(B)\ne 0$. For instance with your sine, whose spectrum is not $0$ at $B=f_0$. But is is only an if. 

Some non bandlimited signals can still be sampled perfectly, under additional conditions. Some signals can be sampled at $B$ even if they spectrum does not vanish at $B$. And some signals can be sampled at a lower rate. Especially when the signal is bandlimited. @JasonR already pointed to Undersampling, and is dealt with in The theory of bandpass sampling, Vaughan et al., and already discussed in Minimum Sampling Rate of Bandpass signal. 

I am not so confident with my understanding of this literature. However, in favorable circumstances with a real bandpass signal, twice the effective bandwidth can suffice, which can be much lower than twice the maximum frequency. And there are other theorems for signals whose spectrum is made of unions of segments of non null frequency.

While mentioning such results, I believe the real issue is different. In some texts, authors assimilate (wrongfully) what they call "the bandwidth" with the distance from the $0$ frequency to the maximum frequency. Especially in texts that do not go into fine details such as the ones stated above and in other answers. 

So in your case, I assume that the difference between the two courses can be explained by laziness or mundane talking.

In practice though, you cannot rely solely on this theorem: it requires you to know in advance the spectrum of a continuous signal, which in many cases you have not idea about. Physical modeling  and analog filtering can help you, but in real life, finite precision quantization, signal jitter, noise and especially finite length signals (which cannot have bounded spectra) forster more precaution and a choice of a sampling frequency sufficiently  higher than twice the maximum frequency (or bandwidth if that applies).

A potential additional lecture: Sampling: What Nyquist Didn’t Say, and What to Do About It.