Excess material from the weld is not making it stronger. If it's a good quality weld, filing it will only make it pretty, not weaker at all. If it's such a poor weld that filing it (or chasing it) will weaken it, then it's about to break already.

The fact is filing and chasing takes more time than welding, so for ten bucks you get it fixed-- if you want it pretty, it's your job to file.

But the bottom line is: If you trust the weld, file away. If you're that concerned, go back by the welding shop and ask them for filing tips.