IA network that is path-consistent, but not consistent
Yes, you are correct.

Here is the classic example of an interval algebra network that is path consistent, but not consistent. It appears in Allen, James F. (26 November 1983) "Maintaining knowledge about temporal intervals". Communications of the ACM. ACM Press: 832–843. doi:10.1145/182.358434.



It seems the arc between interval $B$ and $C$ in the above figure is missing its arrowhead. However, you can assign either direction to that arrow since the relationship $(d\ di)$ is symmetric. 


  It should be noted that this algorithm, while it does not generate inconsistencies, does not detect all inconsistencies in its input. In fact, it only guarantees consistency between three node subnetworks. There are networks that can be added which appear consistent by viewing any three nodes, but for which there is no consistent overall labeling. The network shown in Figure 5 is consistent if we consider any three
  nodes; however, there is no overall labeling of the network. To see this, if we assign the relationship between $A$ and $C$, which could be $f$ or $fi$ according to this network, to either $f$ alone, or $fi$ alone, we would arrive at an inconsistency. In
  other words, there is no consistent labeling with $A-(f)\to C$,
  or with $A-(fi)\to C$, even though the algorithm accepts $A-(f\ fi)\to C$.


I would encourage you to read that seminal paper by Allen for more information.