Not sure if I agree that the budget is way over the top for what you are trying to achieve if the keywords really are 'hyper' competitive. It depends how it has been structured - is it $25k when they achieve the rankings or $25k for the time period (3m, 6m, 1y) regardless of results?
In terms of their plan I agree with the others that sounds of the link building does sound a little low quality but even today those links can still get people ranked highly if done correctly (high quality directories, relevant one way links etc) and the on page stuff is good.
I don't like the way they state how many of each link you will get, that does sounds spammy and automated but there is know way of knowing if the 'one way links' are going to be high quality or not because there is no detail.
To me it all comes down to results - how long have you been with the company and how far have you progressed?