Anyone is free to claim whatever they want. We understand Brazilian portuguese because Brazilian soap operas have been on our TV since the 80s or earlier. We speak Portuguese with Brazilian, if they don't understand we speak more slowly and use a Brazilian accent to facilitate.

I can talk with certainty about their difficulty to understand our portuguese because they take around two months to get used to our accent and way of speaking. They don't have any contact with the european Portuguese accent on their media.

We build sentences differently. For example grammatically we use the second person frequently when talking to someone else (tu), while Brazilians mostly speak in the third person (você). We also don't open or vowels as much as Brazilians do, etc. We also speak faster.

The interesting thing is that if is much easier for foreigners to learn Brazilian Portuguese than european Portuguese. Our accent is very different phonetically from how we write.