Tight Junctions in Cell Types
Tight junctions are very specifically a structure found in epithelial cells, so your teacher is incorrect. Tight junctions are what allow epithelial cells to form a selective barrier between compartments. Fibroblasts can be induced to form tight junctions under certain experimental conditions, but I'm not aware of any case where a skeletal muscle cell expresses a tight junction. Regardless, it would not be normal physiology.

You can read more about tight junctions here, in the online Albert's Molecular Biology of the Cell. This figure from that Chapter illustrates the barrier function.



If you want to get into more of the details re: what we know about the various proteins involved in creating and regulating tight junctions, this is a good review. 

One small correction to your reasoning, though, I wouldn't say the primary purpose of tight junctions is cell-to-cell adhesion, per se, it's selective permeability. These junctions may help the cells to hold together, but the tissues can resist shear stress in knock-out models. A knockout model without a necessary tight junction protein, however, will not maintain selective permeability.