I have some question about the usage of "through" and "outside of". Consider these sentences:
1a. He made transactions through Amazon Payments.
2a. He made sales through Ebay.
3a. He made wire transfers through Bank Of America.
According to some google searches, the opposite of the above sentences is not formed by inserting "not" before "through" like these:
1b. He made transactions not through Amazon Payments.
2b. He made sales not through Ebay.
3b. He made wire transfers not through Bank Of America.
but by replacing "through" with "outside of":
1c. He made transactions outside of Amazon Payments.
2c. He made sales outside of Ebay.
3c. He made wire transfers outside of Bank Of America.
Yet, for this context (Amazon Payments, Ebay, Bank Of America), the dictionary definition of "through" is not really a perfect opposite of the dictionary definition of "outside of". "Through" means "by using". And "outside of" does not quite mean "by not using". Could there be another meaning of "outside of" not found in mainstream dictionaries that would fit the current context?