That is not true, there have been cases where the national constitution had to be amended to follow the EU law.

An Example is the german law which did not allow women to join the millitary till 2000. After that, they had to change the constitution because it does not comply with the EU law about the same treatment of men and women:

https://de.wikipedia.org/wiki/Artikel_12a_des_Grundgesetzes_...

A country can only ignore EU law on the following grounds: - It reduces a right set in the national constitution - It goes against a right set in the national constitution(not if grants more rights or makes rights wider) - It does not fall in the competency of the EU

https://fachinfos.parlament.gv.at/politikfelder/parlament-un...

That article talks about austria and germany specifically, but it should apply to other countries as well.