I'd suggest she waits until at least 6 mos to start solids. As 1) he doesn't really need it (as suggested below) and 2) frankly, solids is a messy thing and why rush into more messes?! ;-)
My 2nd daughter took 2.5 months before she'd eat solids (so at 8.5 mos I finally had some luck). She also is exclusively breast-fed, as I couldn't get her to take a bottle. With the spoon and cereal she'd just push it out with her tongue. When she finally did start taking it I was already moving onto actual solids, and she enjoys feeding herself much more instead (cherrios, fruits, veges, toast, cheese, etc (all cut into pea size pieces). Just this morning I was feeding her yogurt with a spoon and she's still not a fan of the spoon.
On the point of not taking a bottle, I highly encourage your sis to pump and keep trying to bottle feed him with the breast milk every so often -- primarily for the sanity of being able to get away (from the baby) for more than 3 hours at a time!!! I'm now facing transition from breastfeeding to milk/sippy cup at 12 mos old and I fear my DD will have trouble with this.
ADDED: Is the doctor worried about the weight change? I think at 4 mos of age the percentiles aren't totally accurate, and perhaps the weight was taken wrong, thus the wrong numbers? My DD was 17% at 2 weeks, then 47% at 7 weeks, then 22% at 4 mos. I think it might be "normal" for it to fluctuate. I think that may be even more so for a breast-fed baby, as mom's milk is responding to the baby's growth (whereas formula doesn't chg).