There are two different issues here: whether anyone other than the player can suggest a FoRK applies; and whether the GM can mandate that a player FoRKs a skill.
Unlike some systems where there is a short list of skills, each of which covers a clear set of actions, BW has a vast list of skills that overlap in different ways (the Right Skill, Right Time award even suggests finding new and unexpected applications for a skill is encouraged rather than frowned upon). So, while the abstract task mechanism is player states intent and offers skill, GM accepts/rejects the skill, there will be times when a player might know what they want to do but not be certain what skill (or skills) that approach is mechanically because they aren’t their character. Thus, I see no issue with other participants suggesting “that sounds like X” or “if you want to do surgery, you’ll need good light so could FoRK Chandler”.
However, while the GM has to agree a skill applies, it is clear that it is the player’s choice whether to roll or go with a different plan, so whatever anyone (whether GM or other player) says it sounds like is being FoRKed, the player doesn’t have to make those potentially related skills a non-trivial part of the final plan. Therefore, a GM can never require a skill be FoRKed.
A related area is how FoRKs affect consequences of failure, &c. As @ElvisLiving says, these are suggested through the fiction: so, which skills are FoRKed is also a reflection of where the character is more or less competent/experienced/prepared for the unexpected/blasé/&c. and thus can affect consequence of failure; for example, “you can FoRK Evil-wise as part of your argument to the bishop, but if you fail he will wonder how you know so much about the deals demons make.”