I don’t think your policy is unfair as stated. I am assuming that the person cancelled their participation from the group entirely without actually starting the sessions. You scheduled the groups time and the others are prepared to meet at that time. Or even if you had started the sessions and then one drops out, the sessions were booked and on your schedule. If you change the policy for one person, you would be obligated to change it for everyone from that point on.
If this perosn is challenging your policy, you could offer to negotiate a compromise for them. The most I would consider doing is giving them a credit of some portion of their cost toward futute services. Say, 50% of the money paid toward personal training or another group training in the future. You most likely arranged the fee to apply to 4 participants. This person dropping out is not the fault of the other 3 and they should not have to cover this person’s commitment now that this one has changed their mind.