If bachelor theses are a thing in your programme, the statement in question almost certainly is about thesis projects.
However, at least in my experience, most research produces side projects all the time, and a group may just have one that fits your requirements and abilities.
If a group advertises specific projects and does not find a bachelor student, they may also be happy if you are willing to take on such a project (if you bring all the prerequisites).
A very crucial factor in this is whether they expect that your work is worth the resources they invest into you (probably mainly supervision time).
For example, my personal, field-dependent rule of thumb is that the average bachelor project takes as much time to supervise as to do the respective work myself.
Compared to this, you have the advantage that you do not need to supervision for writing and defending a thesis, however, you also have the disadvantage that there is less incentive to make you finish your project.
Another factor playing into this is the kind of work you would do:
Experimental projects tend to require more supervision that theoretical or computational ones, shifting the balance against you.
Thus, the most crucial aspect is that you can convince them that you are capable and willing to complete a small project with a certain degree of independence.
Enthusiasm about what the group in question is actually researching certainly helps in that respect.