Legendary former jockey Sir AP McCoy has called the ban for an amateur rider who finished third at Cheltenham "the worst decision in 25 years".
The 20-time champion, who retired in 2015, said it was "a disgrace" Declan Lavery was suspended for 10 days.
He was one of three jockeys to be punished for what was deemed to be continuing on tired horses in the four-mile National Hunt Chase, a race for amateur riders whose very existence seems in some doubt after more than 150 years.
On Lavery's ban, McCoy, who rode more than 4,300 winners in a record-breaking career, told ITV Racing: "It's an absolute disgrace - it's indefensible."
McCoy is furious with the British Horseracing Authority (BHA) and pointed out that each-way punters - who stood to collect if Lavery's mount finished third - would have been angry if he had pulled the horse up.
"I'm embarrassed for the BHA. Talk about bringing racing into disrepute," he added. "It's wrong. I have never seen as bad a decision in 25 years in racing."
But the BHA, which has introduced a raft of new measures aimed at improving equine safety after six horses died at last year's meeting, vigorously defended the decision.
"It is the responsibility of jockeys to pull up tired horses. This is absolutely fundamental and the rules are clear that priority must be given to the horse if it would be contrary to the horse's welfare to continue riding out," said a BHA spokesman.
"This is why the stewarding panel, which comprises two former jump jockeys, imposed the penalties on the riders."
However, further criticism came from 10-time champion trainer Paul Nicholls, who responded on Twitter to a video of McCoy's comments.
"Spot on AP. I and many other 'professionals' are becoming more and more embarrassed by some of the decisions," said the trainer, who included a 'facepalm' emoji at the end.
In January, McCoy said Uttoxeter stewards' decision to fine trainer Henry Oliver for waving his arms behind one of his runners at the start of a race was "embarrassing rubbish".
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How did we get to this stage?
The BHA and Cheltenham has been under pressure from politicians and welfare groups after six of the 453 horses that ran at last year's Festival suffered fatal injuries.
A seventh horse later died after being injured at the meeting.
This year, favourite Ballyward was fatally injured after his fall at the 17th fence in the National Hunt Chase.
Jockeys have been given daily briefings before racing to outline their responsibilities and warned about overusing the whip.
The four-mile National Hunt Chase, which is restricted to amateur riders, saw just four of the 18 runners finish on the soft-going ground.
Stewards effectively ruled three jockeys carried on riding tired horses that should have been pulled up.
Lavery finished 47 lengths back in third on Jerrysback. Stewards said his mount had made tired jumping errors at the final two fences.
Robert James was suspended for 12 days for his ride on Just Your Type, who fell at the final fence. Noel McParlan, the rider of Mulcahys Hill - a faller at the penultimate obstacle - was given an eight-day suspension.
Post-race examination of the horses did not reveal any abnormalities.
The suspensions are likely to be effective in about two weeks' time.
Stewards also wanted to hold an inquiry into the ride of Damian Skehan on 125-1 shot Clondaw Cian, the fourth of four finishers, but he had left the course and will be interviewed at a later date.
What of the race's future?
Amateur jockeys have been urged to heed official welfare guidelines as doubts begin to surround the future of one of the Cheltenham Festival's oldest races.
The Amateur Jockeys Association of Great Britain (AJA) issued updated guidelines just last week, imploring members to take note of recommendations in the BHA's Cheltenham Festival Review - published in December.
On Wednesday morning, AJA chief executive Sarah Oliver again spelled out the imperative to adhere to the guidelines - noting the future of the race may be at stake.
"That is obviously a major concern," she said of a near 160-year-old race pre-dated only by the Grand Annual as a Cheltenham fixture and which has been run more times than any other.
"Being the oldest historical race, we would hate to see it go - that would be a tragedy."
The AJA's advice became especially pertinent after heavy rain which preceded Tuesday's card and made conditions so testing.
Oliver added: "The ground became more and more holding as the day progressed - and it was inevitable we would end up with tired horses.
"In those circumstances, of course, it is even more important that jockeys follow the guidelines we have published."
Reacting to the riding bans, the BHA said on Tuesday night that "amateur participation in its current form at future Festivals will be under material threat should further incidents occur".
But McCoy said: "I never thought at any stage the jockey [Lavery] did the wrong thing.
"What about each-way punters? The horse's welfare is not an issue - he was perfectly fine this morning.
"What if the first and second horse had fallen? What was the jockey supposed to do then?"
The BHA said it is not the first time this rule has been applied when a rider has finished in the frame.
"All riders were briefed and reminded of their responsibilities before racing, and this included their responsibilities when it comes to pulling up tired horses," a spokesman added.
"The amateur jockeys riding in this race were given a further briefing which covered this issue just before they went out to race."