The word is SIGNIFICANT, which is not as specific as PRIMARY. However, it could be that there would be problems in the Local Authority claiming an interest if the children (or one of them) was living in the house.
I wonder what made the parents make this change. If they approached the solicitor because they wanted to do something to reduce possible care home fees that should be on the solicitor's records and could be used as evidence that they were deliberately trying to deprive themselves of the capital. It would then be much more difficult to avoid a decision to that effect.
The position of the daughter who is on benefits also needs to be considered. Look at para. 6.2 on page 14 of the linked factsheet. She could have benefit problems (she needs to let the DWP know the position, & the local authority if she gets housing benefit), although it may well be possible to argue that at present her interest in the house has no value as no-one would buy her quarter share and no court would grant an eviction order for the house to be sold. If she does have difficulty she should contact the CAB for advice - not the solicitor, who seems not to be very knowledgeable about these matters (he really should have raised it as a possible issue).
I suspect the solicitor may have badly advised your parents - I'm not at all sure anything has been gained by the change.