Yes, I know what you are talking about. If they don't have mixed effects then it is not a mixed effects model.

Perhaps the confusions comes, at times, from what procedure they are using in their software. I can use a mixed effects procedure (e.g., SAS: proc glimmix), try to design the model and end up with out any significant fixed or perhaps random effects. However, I still take the results from the procedure, since you can run a only fixed or perhaps random effects model and the procedure is still controlling for the levels or design (multiple measurements). Then when these results get presented, it appears that the person may have ran a mixed model. I am trying to get better at this, but when presenting your final model you should state if you had random intercepts and effects and be very specific how everythiing was in the model. This way readers know exactly what you did.

Another issue is the lack of consistency in the use of modeling (multilevel, hierarchical, random..., mixed, etc.).