Does the average 40 year old man think he could get 20-25 year old women? Yes, probably.
I get hit on by more 20-25 year old women at 38 then I did when I was 25. I am under no illusion that I am attractive to most women of any age, but certainly -some- young women seem to like me now. I suspect this may be more true for me then some men - I'd guess the characteristics I have may appeal more to women who have a natural tendency to like older men, and maybe aging had more positive impacts on me (I don't so much mean physically) then for some.
My wife's cousin lived in my basement for a while during unemployment. He's in his early 40's and single. Dates mid 20's women all the time.
I think physically men do peak in mid to late 20's, but it seems that the impact of aging reduces their attractiveness far less then it seems to for the average woman. Beyond that, many women seem to value traits that men gain with age more (stability, wealth, power, maturity). Men don't really go out looking for women who are mature and powerful, even when looking for a serious relationship. They look for sweet, kind, loyal and nice to hang out with. Some older women are like this, some younger, but its not something that necessarily is growing with age to offset any decline in looks.
Short version - men get better looking with age a little longer then women do, which isn't surprising given they hit puberty later and are still growing physically into their bodies well into their 20's (compare the performance of 20 vs 25 year old male and female athletes). But its the post-peak impacts that differ more. Women seem to find aging to be less of a negative in terms of male appearance then vice versa. Combined with increased stature, older men may be finding dating easier, and interpret this (and spread the story) that they get 'better with age'. Its probably more accurate to say that many men don't look that much worse as they age and are overall more date-able then when they were younger.