So here's the thing...and I just woke up, so the assessment will be far from perfect.
The BMI site credits a song called French Fries to Dickie Goodman and is published by "Jon Goodman Publishing" (his son). This isn't the only one there that doesn't seem like a Dickie Goodman style track. The Youtube video also credits the son. He's clearly cashing in off his father's reputation - or trying to, anyway. Nothing illegal in that if you inherited the catalog...
Meanwhile, there's an actual picture of the Dick Goodwin track & they both clock in at 2:13. And the track we have has a record needle drop sound suggesting it's the 45 rather than..oh, wait. The YouTube video has it as well.
The Dick Goodwin track doesn't appear on the BMI site even though the 45 photo shows it to be a BMI song. And yes, I looked for "Richard Goodwin", "Goodwin, Richard" and went through all the Goodwins on the site. No "French Fries" by him either when searching for the title rather than the artist. It wasn't on the ASCAP site, either. But it did show that Jon Goodman Publishing is affiliated with BMI.
Best guess: Dickie made the 45 using a similar name, not wanting to be associated with a "non-break in" record. Unless it was successful, of course. When Jon got the rights to his father's catalog, it was time to cash in.
When in doubt, BMI wins out. Find an mp3 of the other track determining them to be separate works & I'll put it back...or make another page. Until then, the cynical "money grab" assessment stands.
I really should have done it this way yesterday...