My DM recently sold her house to someone who was "chain free" and living in rented/with relatives (can't remember which).
DM's onward purchase took bloody ages and we thought it was weird that the buyers weren't pushing. Then their mortgage offer was about to expire and they got really weird and difficult about things.
We had comments like "if you don't exchange tomorrow then the buyers won't be able to exchange until next week because they have young children...." WTF?? That doesn't even make sense! How does having children have any bearing on exchange?? Completion, yes. Exchange???
On the day of completion, their solicitors were giant pricks. Ignored the repeatedly urgent requests from our solicitor. No one knew what was happening or where the money was. Turns out that the money was coming from the sale of another mystery property and that didn't arrive until 3pm in the afternoon. Money didn't hit our solicitors until 4pm, and it was a giant rush to get the money to our vendor in time for it to go through. Mad rush to get the keys at 5.15pm. Very, very nearly didn't make it in time for the bank to process.
Oh, and the buyers then demanded DM paid for a skip the next day because they weren't happy about some stuff my stepdad left behind (he was trying to be helpful - empty garden pots etc because the buyers said they wanted to do the garden and DM/stepdad are downsizing). Buyers hit the roof, I offered to arrange for a collection of anything unwanted in two days time. Not good enough. Buyers demanded collection the same day "because we have CHILDREN". Actually, they have one child who's about 2 years old - I cannot for the life of me see how that's relevant as the garden was left safe and child-friendly.
DM ended up paying £350 for a load of stuff to be removed the same day. Including stuff that belonged in a garden - like ornamental rocks around the base of a tree. There was stuff there that they'd added on, that never came from my DM's house. I think they wanted DM to pay for a skip because they wanted to do some renovation, and thought they could get a skip to use for free. Oh yes, and while all this was going on, my DM had been taken to hospital as she had an accident and then a suspected heart attack but they gave zero fucks. As did the EA who up until this point had been amazing and lovely. He clearly just wanted it sorted - and I suspect he must have known about this mystery property sale but never mentioned it....
So, anyway. They were complete fucking twats about everything and it started with them lying through their arses about where the money was coming from.
I now need to sell my house and I'm dreading it as DM's experience was so bloody awful.
I would pull out and start again OP. Fuck them. If they've lied about this and are being precious now, then judging from my experience with DM's house, there's still a world of pain they could cause you.