Sri Lanka off-spinner Murali, on the verge of becoming Test cricket's leading all-time wicket-taker, was reported to the ICC after the third and final Test against Australia on Sunday by match-referee Chris Broad.
Former England batsman Broad said the bowler's 'doosra', which turns away from the right-handers unlike his stock ball that comes in, needed further examination.
However, under ICC rules, Murali can continue to bowl while his 'doosra' is under initial review.
This is not the first time that Murali's action has been official scrutinised. This latest inquiry led former Sri Lanka captain Arjuna Ranatunga to allege a "white conspiracy" designed to stop Murali, who has 513 Test wickets, following the 28 he took in the 3-0 home series defeat against Australia, overtaking retired West Indies quick Courtney Walsh's world record mark of 519.
Australia leg-spinner Shane Warne finished the series with 26 wickets to take his tally to 517.
Murali's critics have been as vocal as his supporters with legendary India left-arm spinner Bishen Bedi repeatedly dismissing the Sri Lankan's action as akin to that of a "javelin thrower".
But Speed, a lawyer by profession, pleaded for every case to be treated on its merits.
"One of the less appealing aspects of crickets history has been the over-reaction that seems to take place whenever a bowler is suspected of having an illegal action," Speed said.
"There is a danger people will lose all sense of proportion and reason and let emotions override sense," the Australian added.
"The reality is that under the new process put in place by the ICC we are seeing that where problems are identified the intervention of suitably qualified experts helps address the concerns raised."
Muralitharan was three times called for "chucking" by Australian umpires before being cleared by bio-mechanical experts, who concluded that he suffered from a congenital condition that prevented him from straightening his elbow.
Earlier on Wednesday it was confirmed that Murali's 'doosra', would be examined by Australian experts using animation camera technology best known for its work in the Oscar-winning film trilogy 'The Lord of the Rings'.
Perth-based professor Bruce Elliott, an ICC-approved human-movement specialist who tested Murali in 1996, said the advanced technology to be used would deliver a correct and clear-cut analysis of his doosra.
Elliott will use a 12-camera Vicon system which is an updated version of the system used eight years ago, shooting 250 frames per second compared to the six-camera system which captured 50 frames per second.
"It's the ultimate analysis tool, it's the same sort of tool that they use for all the animations in Lord of the Rings," Elliott said.
Elliott, fellow tester Daryl Foster and a third expert will conduct a number of trials while Murali stays in Perth for five days to get an accurate representation of how he bowls.
They expect to finish their report late next week.
They will not test Murali's stock ball - the off-spinner - or his top-spinner, as both were given the green light in 1996 after it was concluded his unique action created an optical illusion that he chucked.
In the meantime Speed defended the ICC's revised two-stage process for dealing with bowlers who had suspect deliveries, pointing out how fast bowler Shabbir Ahmed was "making a successful return to the Pakistan side after remedial work on his action."
And he insisted the ICC would be utterly impartial, no matter who the bowler was.
"The ICC has been asked by all its members to ensure that these rules are followed without fear or favour and we are ensuring that this happens."
Speed's comments came 24 hours after ICC president Ehsan Mani, a Pakistani, dismissed talk of a conspiracy against Muralitharan.
"The match officials are well within their rights to raise any concerns about any delivery from any bowler," Mani said.
"Given this reality it is deeply disappointing to read claims from some quarters about bias."
Murali is the fourth player to be reported to the ICC under its revised process to deal with potentially flawed actions in the past 12 months.
Shabbir, West Indies' Jermaine Lawson and Bangladeshi Sanwar Hossain have already been asked to undergo remedial work on their bowling actions.