The hospital says it happened:
The hospital apologised and said it had had its busiest week since 2016.
Dr Yvette Oade, chief medical officer at Leeds Teaching Hospitals NHS Trust, said: "Our hospitals are extremely busy at the moment and we are very sorry that Jack's family had a long wait in our Emergency Department."
She added: "We are extremely sorry that there were only chairs available in the treatment room, and no bed. This falls below our usual high standards, and for this we would like to sincerely apologise to Jack and his family."
https://www.leeds-live.co.uk/news/leeds-news/lgi-bosses-apologise-after-four-17385357 gives more detail on that quote:
"Our Chief Executive Julian Hartley has spoken to Jack’s mum and offered a personal apology.
"Unfortunately, the unit was also experiencing exceptionally high levels of demand which meant that Jack was required to wait in the clinical treatment room in the Paediatric Emergency Department until a bed became available.
As you've noted, there have been a large number of Twitter accounts claiming it's untrue. Since many of these are clearly copy-and-paste jobs, and political bots are a well-known feature of Twitter, this doesn't carry much weight.
edit: per gnasher729 and TJ Crowder:
A blog alleges that the apparent origin of the counterclaim being pushed by Twitter bots is somebody with family ties to the Conservative Health Secretary.
Guardian and Daily Mail report that she claims her account was hacked and denies the truth of some of the material posted by her account.