Many here don't see a window of attack, the reasoning being that if the (presumably) malicious user gives the wrong email address they lose access to the account. Same outcome if the password gets changed by the recipient of the message. I'd like to offer a glimpse as to a potentially alternate outlook. Maybe it doesn't even apply to this specific situation, it nonethelss has a general relevancy to this conversation.
As an alternative (and sometime supplement) to the regular email/password sign-in, social sign-in is increasingly popular (mainly with OpenID Connect aka Authentication with OAuth2.0). A clear realization by many that have implemented social sign-in has been the separation of concerns between "account management" and "authentication management", which has the natural and arguably convenient side-effect of connecting multiple identifiers to the same account. The way it's done is that registered users are offered the possibility to add alternate sign-in methods to their existing account (e.g. you registered with Google, now you can add Facebook, or email/password).
The multiple login channels feature when correctly implemented with only OpenID Connect is safe since the identifier verification step is always part of the flow. Chances that the owner of the account unwillingly adds a sign-in channel not under their control is slim.
Consider on the other hand a situation where an organization would attempt to offer the same feature with OpenID Connect and their own email/password flow. If they do the latter à la Netflix, that is without confirming that the user owns the claimed email, there's your exploit window.
Malicious user John registers the account using social login (lets say Facebook). He later adds email/password as a login method along with an invalid credit card, but he uses unsuspecting user Jane's email, much like it was done in the Netflix case. Jane receives a message and thinking that it's her account that needs updating she first changes her password as a precaution, before "correcting" her credit card info. All throughout never realizing that an additional social sign-in option is enabled (Facebook).
As previously said here by many, always validate that the user owns the address you're communicating or authenticating with.