Two hallmarks of any good study and any good statistic:
1) produced by random sampling
2) based on a sufficient sample size
The above quoted statistics suffer from a lack of both. In the future a possible solution might be to implement mandatory reporting - this is another topic entirely. However, if this were the case, then we wouldn't be estimating the archery harvest, we would know it (in so far as the numbers represent what respondents claim to have killed or not killed).
Even if we knew exactly how much archery hunters contributed to the harvest in 2011, this in itself would not be sufficient information to decide if archery hunters are exceeding or not exceeding the 15% limit. That's because that statistic is itself a sample from a larger population. Specifically, it is a sample of one of many years. What we need to look at are archery harvest TRENDS, not simply a slice in time (2011). It is possible that archery harvest for 2012 is estimated at under 15%, yet the trend over the years might indicate that we (archers) are tending to exceed the 15% limit.
Several people have already mentioned the issue that the likelihood of kill reporting might differ between gun and archery hunters. This is a major concern, and if we could have an estimate of response rates between the two parties (bow vs. gun vs. bow+gun hunters), then we might be in a position to make some conclusions.
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