Your friend is misremembering technically correct grammar
in the sense that many foreign ESL tests will require students to learn that English has three forms of conditional phrases:
- First conditional: If you join me, I will be honored.
- Second conditional: If you were to join me, I would be honored.
- Third conditional: If you had joined me, I would have been honored.
Essentially they break down into statements about the present or future that are possible but uncertain; statements about the present that aren't thought to be likely; and statements about the past that didn't happen but could have, had things been different.
You'll notice there's nothing unusual about 'would' in the then clauses, which is why @tchrist was defending their existence in the if clauses against the oversimplified ESL test idea that 'would' shouldn't ever appear there.
That said, your example doesn't actually qualify for these ESL forms, because you're not talking about anything that you think is contrary to fact.
...but still completely wrong.
'Would' is technically the past tense of 'will' and was used in conditionals to express the future from the perspective of past events.
If you had joined me [then], I would have joined you [after then but before now; implied '...but you didn't, so I didn't'].
But that sense of 'things could have been different' was too useful and eventually broadened to include cases where 'things could be different'.
42... d. Used in the 1st pers. instead of the normal auxiliary should...
44. a. In a conditional (or equivalent) clause with pers. subject, with implication of intention or volition: = ‘chose to’, ‘were willing to’...
In other words, 'If you would join me, I would be honored' is fine English. It's understood as someone—perhaps British or perhaps falling over themselves a little to be polite—saying
[No pressure. This is purely a hypothetical. I'm just letting you know that,] if [it were the case that] you would join me[, it would also be the case that] I would be honored. [If you did. Which you absolutely don't have to. Sorry to bring it up. Just letting you know. Sooo... Yep. It'd be nice. Thassallimsayin.]
You're just phrasing something that's perfectly possible in a hypothetical way to share some helpful information but to let the other person know that refusal is still perfectly acceptable. (It might still not be, people being how they are, but at least that's what your perfectly grammatical construction is implying and why people use it.)