Symbol rate and bit rate
What Nyquist says is that $$R_p = 2B\,\text{ Bd},$$ where $R_p$ is the number of pulses per second transmitted, $B$ is the available bandwidth, and the units are Bauds or symbols/sec ($\text{Bd}$). Here it is assumed that the pulses being used are sinc pulses; otherwise, the pulse rate will decrease. In this sense, $2B$ is an upper bound on the pulses per second that can be transmitted. It is correct to say that you can transmit two pulses for every Hz of bandwidth available.

Now, each pulse can carry several bits, by means of its amplitude. If you allow, say, two amplitudes (for example, -1 and 1), then each pulse carries one bit and $R_b=R_p$, where $R_b$ is the bit rate. In general, if you allow $M=2^k$ amplitudes, you'll be able to transmit at a bit rate $R_b=kR_p$.

Shannon capacity does constrain the number of bits that you can transmit per second; furthermore, the usual formulation assumes sinc pulses.