McVeigh, who retired from the club at the end of last year, said the players had faith in the club's protocols.
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"We knew that it was 100 per cent above board, and we trust and respect our coaches and doctors who knew about it," McVeigh told AFL.com.au.
"And that if anything was to come of it we'd be absolutely shocked and disgusted."
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McVeigh said the so-called reported 'waivers' were actually consent forms requested by the players from the club assuring all supplements adhered to WADA codes as they moved into a new program.
"We'd never really gone into some of the supplements we were going to take so we asked for a consent form that WADA and the AFL doping code would make sure it was ticked off and that it was in the regulations," McVeigh told SEN.
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"The players got that form in front of doctors, [including] Dr Bruce Reid who has been with the club for over 30 years, and coaches, and everyone knew that this had been ticked off.
"And if you were comfortable with what you were taking, which we all were because it was within the rules and the doctor had told us it was fine…we signed it and it gave them consent to be able to have these tablets."
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McVeigh clarified reports the players were taken away from the club's Windy Hill base to have the injections because the club was searching for a "sterile environment."
"Footy clubs can sometimes be filthy, so we were taken to a sterile environment and the only injection I ever had was a vitamin C or vitamin B injection," he said.
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"At the time I had a little baby girl, I wasn't getting much sleep, I was rundown, I had a bit of a cold, [so] I had a vitamin C injection. [That's] not uncommon. Natural vitamins they are.
"[There was] nothing any more sinister than that, and that's what other players would have if they were feeling a bit down, or trying to get over a cold before a Saturday night game."
McVeigh said he felt sick as the AFL and ASADA investigation was announced on Tuesday, and rubbished Reimers' suggestions about the "odd" supplements the Bombers were taking.
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"Kyle Reimers has come out and said some things that are untrue," he said.
"He's a disgruntled player that was delisted by the football club that very rarely turned up to pre-season training in any sort of form that resembled a professional footballer.
We were taking very odd stuff: Reimers
"[And] the stuff he said [about] 'We didn't know what we were taking'. Every player knew what they were taking. It was listed and we knew that it was within the rules.
"It was clearly stated to us what we were taking. If you didn't know, you must have been asleep in the meeting, which, you know what, Reimers probably was."
McVeigh, who played 232 games for the club between 1999-2012 and is a close friend of coach James Hird, expected the investigation to come up clean.
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"I think the players will be 100 per cent fine. I think they'll find that what they were given were well within the rules," McVeigh said.
"I can't speak for any outside influences that may have gone into the club, but I think all players who were involved in this - vitamins supplements, you've got to make that clear, and in a sterile environment - I think they'll be fine."
Click here to see the Essendon timeline from June 2011
Follow AFL website reporter Callum Twomey on Twitter at @AFL_CalTwomey.
