From what I've read, what your clinic says is true - the earlier they are frozen, the better they thaw. There are other factors though. There are 2 methods of freezing - the slow method and vitrification. Vitrification has a better thaw rate than the slow-freeze method. The clinic's experience and skill also comes into play as it seems to be a bit of an art and some embryologists are just better at it than others.

We have had 3 frozen (slow-freeze method) embryos thawed. Two were frozen on day 2 and only 1 of those two survived the thaw and it lost a cell in the process. The third was frozen on day 3 (different IVF cycle) and it survived the thaw with all cells intact. I don't think either of them divided between thaw and transfer. Both of our FETs were BFN, but we have egg/embryo quality issues.