I suggest this is down to the contractual agreement between you. If the client has a clause written into the contract that documentation will be to the client's own standards, then the supplier must comply. If not, then the supplier may be able to use their own standard format.
The main difficulty that I would perceive is when the client has to approve the requirements document, and this is presented in a format that is not familiar to the client. It may lead to extensive discussions to allow both parties to agree that all requirements have been defined (or not), as some of the requirements may be in different parts of the document, or expressed in different and unfamiliar ways. Depending on the complexity of the requirements, and the number of people within the client team who have to approve the document, you may find that this extends the approval process significantly.
If you are from the supplier side, it would be worth asking the client PM why he or she wants the requirements in a specific format, and why the supplier's standard is not acceptable. If the reason is that the documentation is retained in a repository where all requirements across multiple projects are held in a consistent format, then they may have a strong justification for asking for their standard to be adhered to. However, in my experience, many companies define a standard then allow deviation from it if it is expedient to do so, therefore the "standard" may be more of a target than an absolute necessity.