Personally, I'm not against considering the size of the pot -- if the rule suggests that we have to determine what is "reasonable", then I don't see why we should be constrained in the factors that we use to determine what is reasonable or not. If a strict application was to be enforced (i.e. if "3" would ALWAYS be considered 300 whenever the big blind is less than 300), then I doubt it would have been necessary to even add the word "reasonable" to the rule.
Another factor that I think one should definitely consider is the action in the current betting round. So for example, if blinds were 75-150, someone raised to 600, and then the next player said "3", I'd be much more likely to view this as 3K than an undercall of 300.
The fact that the player threw in 2 1K chips first, suggesting that the bet is on the order of 1000s rather than 100s, can also be a relevant factor; however, I personally would put less weight on this. The only question in my mind is whether 300 is a reasonable wager or not at the point the verbal declaration is made -- i.e. before chips are put into the pot --, and apply the rule accordingly. Otherwise, you may get into situations where a player could alter the bet by putting in 1K chips instead of 100 chips after getting a read, for example, if both are legal wagers.
So I think it's OK to take whatever factors you think are relevant into account to determine "reasonableness". But if there's doubt in your mind, I'd go with the lesser amount.