I read "place you at the highest comp package they can" to mean "place you at the employer that will give you the highest comp package they can". So if they think you're good enough for clearlydoomed.io who pay 175k and GigaTech who pay 200k, but not Risk Securities who pay 300k, they will push you towards MegaTech.
It depends. "they can" is doing a lot of work in the original claim.
If A, B and C are the companies involved, with respective pay rates of 175k, 200k and 300k, it's still going to be better for the recruiter to try you at all three, because that is very little extra work for the commission involved.
However, if B is more circumspect about hiring and always takes a month to make a decision while always A comes back with "go/no-go" in 2 days, then its better for the recruiter to take the 1.75k commission and move on to the next candidate, rather than hold out a month for a $2k commission that may not happen while the 1.75k commission is lost because A has a quick turnaround time. In order for them to do this, they have to mislead you about your chances with B, or have to completely hide the option of B from you, because they know that you, personally, would hold out a month for an extra 25k.
Business and sales is all about cashflow. It's better to conclude your business today with a profit of $1.75k rather than in a month with $2k.
As far as the $3k commission goes, the recruiter is almost definitely not going to wait a month either, unless, in their experience, you're so far and beyond the best candidate for that position that it's a slam dunk. That is highly unlikely.