For an apology to be impactful it must have three important components. Firstly, it must be honest (and must also seem as genuine as it really is). Secondly, it must show self-sacrifice (which implies that the company or person making the apology must make a statement for the public good). And lastly, it must be done with the right attitude (which implies that it must be made in time & in the right manner).
Even if one of these three aspects is missing from the apology, the apology becomes counter productive and often deteriorates the image further. When organizations willingly or unknowingly commit errors, the act almost always erodes the trust the stakeholders have painstakingly built and placed on the organization. This is because such errors question two more fundamental building blocks of Trust, namely Competence (if the error was unintentional as in Toyota's case) and/or Intent (in case the error was intentional as in Satyam's case). Unfortunately, in the case of Toyota, the unintentional technical error was compounded by inaction and delay which almost made the lack of action 'intentional', and therefore showed lack of proper intent of Toyota, adding to its PR woes.
Especially in cases like Toyota, an apology would have been the most important tool to mitigate this Trust crisis. This is because 'acceptance of a wrong' showcases audience empathy, and also helps rebuild a non-threatening ambience (which allows the stakeholder to begin the process of building 'Trust' yet again)- another essential in creating stakeholders capacity to trust the company.
In fact, the apology is almost a clinical solution to errors, but if its substituted with the placebo of a plain 'acceptance' of the error, its impact will almost always be negligible.
Endnote: Studying 'Apology' further, the impact of apology is so strong that, strangely enough, an apology even without a transgression creates a very positive influence over the target. If, however, one can find a reason for an apology (without sounding ridiculous) without a reason to be apologetic, it is more likely to exert positive influence over the target. Typical examples of this are in the use of terms like ‘I’m sorry to be troubling you…’ are likely exert a better influence on the target.
(Update on 9th May 2012: This article and more in this blog became the basis for chapters in my forthcoming book 'Decoding Communications'. Please visit http://decodingcommunications.blogspot.com to see the progress of the book)