Not an expert, (but with a strong opinion ),
When Anderson says there's "no documentary evidence" he's not saying that the baptism is invalid, but that it doesn't document that Daniel Abbott the immigrant was born in 1584 in Biddleston to those parents. While the fact itself needs to be verified, if it's for the wrong person it's not really relevant. A fake baptism and a real baptism for the wrong person are both wrong. (Also, I'd say while not impossible, the date might be a little early to be immigrant Daniel...in fact its early enough that Daniel bp 1584 could even be the immigrant's father.)
We all want to find the answers and fill in that empty spot on our tree. So confirmation bias is strong. You have to actively work against it.
Take a step back and look at the bigger picture. Keep in mind...for any given baptism in England at that time, its more likely that person died young or stayed in England. Indexed online records are so helpful, but they are isolated from their context. I've seen quite a few coincidental baptisms used as a source to connect parents, only to have a corresponding burial record for the same child turn up once the full parish records are examined. (And yet those relationships persist on online trees).
Some questions to think about when evaluating the likelihood that is Daniel the immigrant's baptism record:
How many parishes existed in East Anglia in that 25 year range (1585-1610)? How many of those parish registers were destroyed? How many are available online? How many have been indexed? How many births of that time went unrecorded? How many deaths went unrecorded?
How common is the name Abbott? Is it geographically isolated or widely distributed? How common is "Daniel" at that time? How common is Daniel within Abbott families?
Are there any clues in the immigrant's record that would indicate class or a better estimate for his age?
You could certainly create profiles for the parents and research their family. Perhaps a will or a deed will turn up within the extended family and provide some indication either way. But keep in mind that there's a good chance you're researching an unrelated family. (But could be helpful to someone else). Be sure to document evidence that proves and disproves the theory.