and even then says it applies to transactions without a fee - ie, begger transactions.
I have to say that I've never heard of the term "begger transactions". If all miners cared about was maximizing profits, we'd probably have mostly empty blocks.
Yep, fortunately it's not the only thing we worry about, which is why Eligius still uses the largest block size of any pool to date (most others limit to some arbitrarily low number), mines transactions with a reduced fee schedule from the reference client, mines some non-standard transactions, and other things helpful to the network as a whole that most other pools don't care to put any effort towards which have nothing to do with miner profits.
I'm not sure why your partner would refer to transactions with no fee (or even with a fee less than 0.1 "TBC", as I understand it) as "begger transactions" then.
By the way, how is someone supposed to submit a low-fee transaction to Eligius? I believe the direct submission form was taken down.
Not sure on the "begger transaction" thing, but I suppose it makes some sense in context. I assume it's also a reference to the small spam transactions that split into 100+ tiny outputs and the like, essentially pointless transactions.
As for transaction submission, most Eligius servers (*.eligius.st) will accept a P2P connection on a public bitcoin node that will accept the transactions, which has been sufficient for most since before and after I disabled the never-really-supported pushtx page that was being abused.