No, the Vine is not a requirement for casting the spell. Only for extending the range of the spell beyond what is printed on the card.
The Samara Tree can cast a Seedling Pod with or without the use of a Vine token. The Vine token is only required if you want to cast the spell beyond the range printed on the card. So, you can cast the spell in range 0 to 1 zone of the Samara Tree without using a Vine token.
This rule applies similarly for when the Druid is casting the spell.