That is what the politicians opposing the independence say. And the fact that Spain wants to discourages those movements says a lot about Spain and it increases my understanding for the desire to become independent.
There are also people who say this
(wiki):
Former European Court judge, Professor Sir David Edward, argued in a December 2012 paper that
both Barroso and the SNP were incorrect. Given
the situation would be unprecedented and the absence of any express provision in existing EU treaties on how to handle the situation, he stressed the "obligations of good faith, sincere cooperation and solidarity" in the EU treaties, arguing that lengthy negotiations would have to take place but that these would do so prior to the date of independence and that they would lead to a treaty amendment rather than an accession treaty.
Roland Vaubel, a member of the Advisory Council to the German Federal Ministry of Economics and Technology, published a paper in May 2013 titled
The Political Economy of Secession in the European Union, which stated that Scotland would remain a member of the European Union upon independence. The paper suggested that there would need to be a negotiation between the Scottish Government and the British Government on "how they wished to share the rights and obligations of the predecessor state". Vaubel also stated that Barosso's comments on the status of Scotland after independence "has no basis in the European treaties".
Professor Lars Bo Kaspersen, Head of Political Science at the University of Copenhagen, said that he believed independence "could be a fairly quick transition". He continued: "I'm sure that the European Union in general would strongly support Scottish membership and the same goes for NATO. I can’t think of anyone who wouldn't think it was a good idea."
(This last professor is obviously wrong with his last sentence, but I don't think Spain alone can stop all this)