Yes, of course you are right. But see, In a course like this I'm trying to introduce what 'relativistic' means. A magnetic field is relativistic in the following sense:
If observer A sees just a magnetic field, then observer B (moving relative to A) sees an extra electric field1
. This leads to the idea that forces are relativistic. Students thought they weren't. Well if forces are relativistic, then other observables might be, too. Like space and time, themselves. That's why I think it's an entry point (at school...).
Yes I know the magnetic field is also different - but of higher order in v/c - no need to analyze this here.