I would find that very, very hard to believe. I spent 24 days in the Dornoch area in May & June and, while I did not get to play Brora, I heard no talk about the club being in trouble.
In fact, there was an article in the Northern Times paper in early June about the relatively high-profile club pro that had recently come to work at Brora. I believe he was a past president of the Scottish PGA or something along those lines.
In addition, there was a very successful development of 24 holiday apartments built a year ago overlooking the course, on the site of the old Links Hotel. In fact, the demand for these apartments was so great, another development nearby is planned.