If your investor demands a put option, then consider countering with a request for a call option.
On one of my deals, the lead investor wanted a put option at year 6 (at FMV as determined by a mutually-agreed-upon appraiser). As an exchange, I asked for a call option in year 7, which they accepted.
Options have value (hey, Black-Scholes). In this case the company would get the right to repurchase ~20% of its stock, which would be super valuable if the FMV failed to reflect true market conditions and/or future prospects.
