It matters a LOT. A you-said they-said dispute over a verbal contract can be expensive to resolve --- almost certainly way more expensive than the total value of this dev contract.
Startups who hire outside vendors should be very careful to foreclose on any potential verbal contract --- "do not start working for us until we have a signed master agreement and a statement of work" --- and that's for a lot of reasons, not just misunderstandings like this.
Obviously, if a company operator deliberately leads a vendor to believe there's an authorization to start work, they're morally on the hook for billed hours. But in reality, consultants go into engagements like that knowing that they're on the hook if anything goes wrong. This comes up a lot in consulting, because legal negotiation over master agreements can take weeks and sometimes threaten to ice deals that can be kept alive by just starting ahead of the contract.
But it's not a verbal contract if it's over email, right? It's right there in writing, we both have copies of it, it can (theoretically) be verified by a third party.
If I go to small claims with a copy of an email, what can they say that they couldn't say just as well if I go in with a piece of paper I claim they signed?
I've never seen someone say "Don't start working without a notarized contract", but that's the hidden message, right? Otherwise we're just playing at semantics.
Edit: As above, I notice now the OP did have a purely verbal contract. I was referring to emailed agreement which is common in our line of work, though.
It is worth noting that there are reasons beyond enforceability for having written contracts - making sure both parties are on the same page about important elements of the contract such as scope of work, deliverables, acceptance criteria, and payment terms.
I'm not implying that this is what happened here, but it isn't at all uncommon for two parties to verbally negotiate something like this in good faith and come away with different understandings of subtle, but important, elements.
Writing it down doesn't prevent this entirely, but it goes a long way to clearing up possible misunderstandings.
Certainly, nobody deserves to go unpaid for their work, but anyone starting work without a clear written understanding of the facts is setting themselves up for all sorts of problems.
Startups who hire outside vendors should be very careful to foreclose on any potential verbal contract --- "do not start working for us until we have a signed master agreement and a statement of work" --- and that's for a lot of reasons, not just misunderstandings like this.
Obviously, if a company operator deliberately leads a vendor to believe there's an authorization to start work, they're morally on the hook for billed hours. But in reality, consultants go into engagements like that knowing that they're on the hook if anything goes wrong. This comes up a lot in consulting, because legal negotiation over master agreements can take weeks and sometimes threaten to ice deals that can be kept alive by just starting ahead of the contract.