Yes, it is possible that some of your students are reaching compression in the front of the vertebrae when they flex the spine forward: as we get older, many people start to grow osteophytes (bone spurs) all around the edges of the vertebrae (this is also called osteoarthritis). You can see an example of it here
. Notice how this woman’s lumbar vertebrae have growths in the front: this could potentially stop her from flexion in that region. If this is the case, and compression is stopping them, there is no way to go further, so there is no way to stretch the tissues along the back side of the spine. Maybe they could go around it a bit: try flexions with twists or side bends: that could move the points of compression away from each other and allow perhaps a bit more range of motion. Think of ½ Butterfly for example: it is a bit of a twist and side bend as well as a forward fold.
However, I suspect that what is actually stopping your students is still tension along the posterior side of the spine. Your students may not be attuned to feeling the stresses there though. You may want to help them build that ability. What do they feel in Cat/Cow? Can they get their spine raised up in the Cat pose? What is stopping them then? One exercise is to palpate the spines in various poses: they can do this as partners, or you can do it for them. In a simple sitting posture, touch each of the spinous processes along the spine. This is the neutral position. Then do a twist or a Cat: now palpate the spinous processes to help the student feel them. Do another pose, and again palpate. This will help bring their own awareness to this area: it is a pretty deep practice! Can you feel your own spinous processes and notice how they change their positions in different postures? It may help your students feel what is going on along their spine and in their back while practicing.
There is another possibility: for some people, their spine fuses as they age. The joint is lost and no movement is available. There are other pathologies that can also do this: degenerated discs, for example: there is less space now in the joint for flexion. If there is any pain when your students do these poses, they should seek professional guidance.
I hope this helps.