Well, yes... You'll need it to run on servers you can trust. Otherwise server can make it look like you received a payment when you didn't.

Going further, I really don't see why you would want to bloat Bitcoin blockchain with data... Basically, you just need to timestamp messages, and there is much less wasteful way to do it.

E.g. you can put all these data-transactions into a Merkle tree and timestamp only root of that Merkle tree. Or you can use a merged-mined alt-chain.

Let's summarize You use Bitcoin for two things: secure timestamp via proof-of-work, and storage of data. Storage of data is expensive.

Thus you can drastically reduce costs if you store data elsewhere.