I'm a celebrant. I'm in Scotland so I can hold legal weddings, but we also have similar situations to the one the OP described.
If I am holding a non-legal commitment / blessing ceremony, I am always clear with the couple that I will not lie, and that if someone asks me a question then I must answer truthfully. It is a legal offence to pretend to solemnise a marriage when you are not actually doing it.
The words that I use during the ceremony are also different. I might say that "we're here to witness X and Y make their personal vows to each other" but I would never say "we're here to witness their marriage" (because we're not). Also I cannot make the legal 'pronouncement of marriage' so that has to be different. And it is illegal to sign something that is a replica of a marriage certificate.
During the marriage preparations and discussions with the couple I ask about the legal element of their wedding (if I'm not doing it) and who knows. Tbh I don't much care about the next door neighbour or the long lost school friend and what they've been told, but I always counsel the couple to tell close family and the bridal party, and I would decline to hold a ceremony where only the bride and groom knew. I would not be part of 'hoodwinking' the family and I could lose my authority to practice if I did.
Because I can hold legal ceremonies, I am aware of the legal implications of what I do. However there are many organisations that train celebrants and not all of them are good. So essentially anyone can attend a weekend course set themselves up as a celebrant, but they may not have been schooled in what they can and can't say during a 'wedding' ceremony, and they may not understand the risks they are taking.
In OP's situation, I think OP was foolish not to tell parents etc. The marriage certificate is dated for the legal wedding, the marriage is a public record and people could find out in all manner of ways.
However I also think the celebrant was at fault, not for what they said at the ceremony, but for not spending time explaining to the couple that they would not be able to lie, and for not counselling them about the risks.