The statement that Sections 124 and 125 of the Indian Contract Act, 1872, are not exhaustive of the law of indemnity is accurate and widely accepted in legal jurisprudence. To understand this, it's essential to first grasp the core concept of indemnity and then analyze the scope and limitations of these sections.

Concept of Indemnity: Indemnity, in its essence, means to make good a loss. A contract of indemnity is one where one party (the indemnifier) promises to save the other party (the indemnity-holder) from loss caused to them by the conduct of the promisor himself, or by the conduct of any other person.

Sections 124 and 125 of the Indian Contract Act, 1872:

• Section 124 (Contract of Indemnity): This section defines a 'contract of indemnity' as a contract by which one party promises to save the other from loss caused to him by the conduct of the promisor himself, or by the conduct of any other person. This definition is notably restrictive, as it limits the scope of indemnity to losses arising from human agency. It does not explicitly cover losses arising from accidents, natural calamities, or acts of God, which are typically covered under the broader English common law understanding of indemnity.
• Section 125 (Rights of Indemnity-holder): This section enumerates the rights of an indemnity-holder when sued in respect of any matter to which the promise to indemnify applies. These rights include recovering all damages, all costs, and all sums paid under a compromise, provided the indemnity-holder acted prudently and within the scope of the indemnifier's authority.

Why Sections 124 and 125 are Not Exhaustive:

1. Narrow Definition of Loss: As mentioned, Section 124's definition is confined to losses caused by human conduct. This is a significant limitation compared to the English common law, which recognizes indemnity for losses arising from any cause, including natural events or accidents. Indian courts, however, often refer to English common law principles to interpret and apply indemnity in a broader sense.
2. Implied Indemnity: The Indian Contract Act primarily deals with express contracts of indemnity. However, the law recognizes 'implied indemnity' arising from the circumstances of a case or by operation of law. For instance, in relationships like principal and agent, master and servant, or co-sureties, an implied promise to indemnify can arise. These situations are not explicitly covered by Sections 124 and 125 but are recognized and enforced by Indian courts based on equitable principles and common law.
3. Equitable Principles: Beyond the statutory provisions, the principles of equity play a crucial role. Courts often apply equitable principles to enforce indemnity, especially in situations where a person is compelled to pay money that another person is legally bound to pay. This ensures fairness and prevents unjust enrichment.
4. Rights of Indemnity-holder (Beyond S. 125): While Section 125 outlines specific rights when the indemnity-holder is sued, equitable principles allow an indemnity-holder to sue for specific performance even before actual loss occurs, particularly if the indemnifier's liability has become absolute. This pre-emptive right is crucial to prevent the indemnity-holder from suffering financial ruin while waiting for the actual payment of loss, a concept not explicitly detailed in Section 125.

Conclusion: Therefore, the statement is correct. Sections 124 and 125 of the Indian Contract Act, 1872, provide a statutory framework for express contracts of indemnity but do not encompass the entire gamut of the law on indemnity. The broader principles of common law, equitable considerations, and judicial interpretations have expanded the scope of indemnity in India to include implied contracts and a wider range of losses, making the statutory provisions non-exhaustive. This comprehensive approach ensures that the spirit of indemnity – making good a loss – is upheld in various contexts not explicitly covered by the Act.